1) Problem #PRAESQ4 "PRAESQ4 - Watch Introduction to Binomial RV Video" |
Take out your notebook, then watch the video - Introduction to Binomial Random Variables. Write a short reflection of what you learned from the video. © STATS4STEM.ORG |
Ungraded Open Response: |
2) Problem #PRAER43 "PRAER43 - Binomial Experiment - Characteristics - OLI" |
A)
Let's consider a few random experiments. In each of them, we'll decide whether the random variable is binomial. If it is, we'll determine the values for n and p. If it isn't, we'll explain why not. A fair coin is flipped 20 times; X counts the number of heads. Can this be considered a binomial experiment? © STATS4STEM.ORG |
Multiple Choice:
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B)
A fair coin is flipped 20 times; X counts the number of heads. Determine the value of n. |
Algebraic Expression:
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Hints: |
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C)
A fair coin is flipped 20 times; X counts the number of heads. Determine the value for p. |
Algebraic Expression:
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Hints: |
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D)
You roll a fair die 50 times; X is the number of times you get a six. Can this be considered a binomial experiment? |
Multiple Choice:
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E)
You roll a fair die 50 times; X is the number of times you get a six. Determine the value of n. |
Algebraic Expression:
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Hints: |
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F)
You roll a fair die 50 times; X is the number of times you get a six. Determine the value of p. Give answer as a percentage rounded to the nearest whole number. Do not include % sign. |
Algebraic Expression:
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Hints: |
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G)
Roll a fair die repeatedly; X is the number of rolls it takes to get a six. Can this be considered a binomial experiment? |
Multiple Choice:
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H)
Draw 3 cards at random without replacement from a set of four cards consisting of one club, one diamond, one heart, and one spade; X is the number of diamonds selected. Can this be considered a binomial experiment? |
Multiple Choice:
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I)
Draw 3 cards at random with replacement from a set of four cards consisting of one club, one diamond, one heart, and one spade; X is the number of diamonds selected. Sampling with replacement ensures independence. Can this be considered a binomial experiment? |
Multiple Choice:
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J)
Draw 3 cards at random with replacement from a set of four cards consisting of one club, one diamond, one heart, and one spade; X is the number of diamonds selected. Sampling with replacement ensures independence. Determine the value of n. |
Algebraic Expression:
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Hints: |
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K)
Draw 3 cards at random with replacement from a set of four cards consisting of one club, one diamond, one heart, and one spade; X is the number of diamonds selected. Sampling with replacement ensures independence. Determine the value of p. Give answer as a percentage rounded to the nearest whole number. Do not include % sign. |
Algebraic Expression:
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Hints: |
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L)
Approximately one in every 20 children has a certain disease. Let X be the number of children with the disease out of a random sample of 100 children. Although the children are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent. Can this be considered a binomial experiment? |
Multiple Choice:
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M)
Refer to the previous problem, determine the value of n. |
Algebraic Expression:
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Hints: |
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N)
Refer to the previous problem, determine the value of p. |
Algebraic Expression:
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Hints: |
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3) Problem #PRAESQ5 "PRAESQ5 - Calculating Binomial Probabilities - Video" |
Please watch the video - Calculating Binomial Probabilities. This video is long, you don't need to watch the whole video from start to end - You can if you want, however, feel free to skip parts that you feel that you understand. An error was made in the video => 4!=4*3*2*1, NOT 3*2*1 Write a reflection on what you learned from the video. © STATS4STEM.ORG |
Ungraded Open Response: |
4) Problem #PRAESVN "PRAESVN - 134148 - What is 8 choose ..." |
What is 8 choose 3? In other words, if you have 8 trials, how many different ways can you order 3 successes? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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5) Problem #PRAESQ7 "PRAESQ7 - OSB - Question 5" |
A)
A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads? Round decimal to thousandths. © STATS4STEM.ORG |
Algebraic Expression:
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Scaffold:
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Scaffold:
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B)
A fair coin is flipped 9 times. What is the probability of getting exactly 2 heads? Round decimal to hundredths. |
Algebraic Expression:
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Hints: |
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6) Problem #PRAETAV "PRAETAV - Binomial Probability - Calculating by hand" |
A)
Recall how to calculate Binomial Probabilities: By hand, if X ~ B(13, 0.6), calculate P(X=7). Give answer as a decimal rounded to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Scaffold:
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Scaffold:
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Scaffold:
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Scaffold:
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B)
A teacher has 30 students. If the probability of having a student absent is .05. Find the probability that at least 1 student is absent on any given day. Assume student absences are independent events. Give answer in decimal form rounded to the nearest hundredths. |
Algebraic Expression:
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Hints: |
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P(ALL 30 students are present) = 0.9530 = 0.2146 |
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C)
A teacher has 30 students. If the probability of having a student absent is .05. Find the probability that 2 students are absent on any given day. Assume student absences are independent events. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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7) Problem #PRAES3Z "PRAES3Z - Calculating Binomial pdf and cdf - using maconstate.edu" |
A)
Learn how to use the TI-83 by walking through the following three examples on this page. http://calculator.maconstate.edu/1200_binomial_lesson/page1.html To find probabilities of the type P(X = x) or P(X ≤ x) using the TI-83, we'll use the following function: binompdf(n, p, x) = P(X = x) binomcdf(n, p, x) = P(X ≤ x) where: n is the number of independent trials p is the probability of success on each trial x is the number of successes in trials Using your TI-83, if X~B(11,0.7) find P(X = 7). Give answer as a decimal rounded to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
Using your TI-83, if X~B(8,0.7) find P(X < 6). Give answer as a decimal rounded to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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8) Problem #PRAETAP "PRAETAP - Binomial pdf and cdf using R - OLI" |
A)
Binomial probabilities using R. To find probabilities of the type P(X = x) or P(X ≤ x) in R, we'll use the following function: dbinom(x, n, p) = P(X = x) pbinom(x, n, p) = P(X ≤ x) where: x is the number of successes in trials n is the number of independent trials p is the probability of success on each trial Now, lets consider a scenario where a student takes a test with ten questions. The probability of getting any question correct is .2 (the student apparently didn't study!). Using R, find the probability that the student gets exactly 4 questions correct. In other words, find P(X = 4). Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
dbinom(4, 10, .2) |
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B)
Now use R to find the probability that the student gets no more than 4 questions right, P(X ≤ 4). Give answer as a decimal rounded to the nearest hundredth. |
Algebraic Expression:
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Hints: |
pbinom(4, 10, .2) |
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C)
Now lets assume the probability of getting an answer correct is .4, and there are now 20 questions on the test. Using R, find the probability that the student gets at least 7 questions right. Give answer as a decimal rounded to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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1-pbinom(6, 20, .4) |
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9) Problem #PRAETDP "PRAETDP - 134645 - On average 5 in 8..." |
On average 5 in 8 people like a certain movie. If you randomly select 5 people, what is the probability that at least 4 will like the movie? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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P(X≥4) = 0.38 (ROUNDED) |
10) Problem #PRAETAA "PRAETAA - Binomial Probability - cdf - OSB #6" |
When Susan and Jessica play a card game, Susan wins 60% of the time. If they play 9 games, what is the probability that Jessica will have won more games than Susan? Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Scaffold:
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Scaffold:
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Scaffold:
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Scaffold:
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Scaffold:
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11) Problem #PRAEU3Y "PRAEU3Y - 136266 - A student takes a..." |
A)
A student takes a 10-question, true/false exam and guesses on each question. Find the probability of passing if the lowest passing grade is 6 correct out of 10. Round answer to nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
In a survey, 30% of the people interviewed said that they bought most of their books during the last three months of the year (Oct, Nov, Dec). If nine people are selected at random, find the probability that exactly 3 of these people bought most of their books during October, November, and December. Round decimal answer to the hundredths. |
Algebraic Expression:
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Hints: |
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C)
Refer to the previous problem. If nine people are selected at random, find the probability that at least 4 of these people bought most of their books during October, November, and December. Answer as decimal rounded to nearest hundredth. |
Algebraic Expression:
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Hints: |
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D)
In a survey, three out of four students said the courts show "too much concern" for criminals. Find the probability that at most three out of seven randomly selected students will agree with this statement. Round decimal answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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12) Problem #PRAEU36 "PRAEU36 - 136272 - R.H. Bruskin Asso..." |
A)
R.H. Bruskin Associates Market Research found that 40% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is selected, find these probabilities. a) Exactly two people will agree will agree with that statement. Round this answer and all subsequent answers to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
b) At most three people will agree with that statement. |
Algebraic Expression:
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Hints: |
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C)
c) At least two people will agree with that statement. |
Algebraic Expression:
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Hints: |
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D)
d) Fewer than three people will agree with that statement. |
Algebraic Expression:
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Hints: |
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13) Problem #PRAEVTK "PRAEVTK - 136967 - Go to www.bls-sta..." |
Go to www.bls-stats.org - click on videos and watch video titled: Binomial Coefficient Calculation By Hand. Did you watch the video? © STATS4STEM.ORG |
Multiple Choice:
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14) Problem #PRAEVTG "PRAEVTG - 136964 - By hand, calculat..." |
By hand, calculate 5 choose 3. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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15) Problem #PRAEVTF "PRAEVTF - 136963 - Go to www.bls-sta..." |
Go to www.bls-stats.org - click on videos and watch video titled: Calculating Binomial Coefficient and Factorials Using TI-83. Did you watch the video? © STATS4STEM.ORG |
Multiple Choice:
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16) Problem #PRAEVTH "PRAEVTH - 136965 - Using your TI-83,..." |
17) Problem #PRAEVPY "PRAEVPY - 136855 - An article in USA..." |
A)
An article in USA Today stated that "Internal surveys paid for by directory assistance providers show that even the most accurate companies give out wrong numbers 15% of the time." Assume that you are testing such a provider by making 10 requests and also assume that the provider gives the wrong number 15% of the time. Round this and subsequent answers to the nearest hundred. a) Find the probability of getting one wrong number. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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TI-83 => binompdf(10, .15, 1) R/Rweb => dbinom(1, 10, .15) |
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B)
b) Find the probability of getting at most one wrong number. Round to the nearest hundred. |
Algebraic Expression:
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Hints: |
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R/Rweb => pbinom(1, 10, .15) |
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18) Problem #PRAEVP5 "PRAEVP5 - 136860 - About 70% of Face..." |
A)
About 70% of Facebook users are outside the United States. If 100 users are randomly surveyed, find the probability that: a) At least 75 are from outside the United States. Do not use the normal approximation to the binomial for these problems (or your answers may not match) and round this and subsequent answers to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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R/Rweb => 1-pbinom(74,100,.7) |
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B)
b) Exactly 71 are from outside of the United States. Round to nearest hundred. |
Algebraic Expression:
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Hints: |
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R/Rweb => dbinom(71, 100, .7) |
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C)
c) At most 80 live outside of the United States. |
Algebraic Expression:
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Hints: |
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P(X≤80) = binomcdf(100, .7, 80) R/Rweb P(X≤80) = pbinom(80,100,.7) |
P(X≤80) = 0.9911128
Answer = .99 (ROUNDED) |
D)
d) Less than 64 live outside of the United States. |
Algebraic Expression:
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Hints: |
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R/Rweb => pbinom(63,100,.7) |
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E)
e) Less than 65 or more than 72 live outside of the United States. |
Algebraic Expression:
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Hints: |
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TI-83 => binomcdf(100, .7, 64) R/Rweb => pbinom(64,100,.70) ----------------------------------------- 1 - P(X≤72) TI-83 => 1-binomcdf(100, .7, 72) R/Rweb => 1-pbinom(72,100,.7) |
pbinom(64,100,.70) + (1-pbinom(72,100,.7)) [1] 0.4124448 Answer = .41 |
19) Problem #PRAEVTD "PRAEVTD - 136961 - Go to www.bls-sta..." |
Go to www.bls-stats.org - click on videos and watch video titled: Binomial - Mean & Std Deviation & Normal Approximation. Write a short reflection on what you learned. © STATS4STEM.ORG |
Ungraded Open Response: |
20) Problem #PRAEVQC "PRAEVQC - 136867 - About 70% of Face..." |
A)
About 70% of Facebook users are outside the United States. In a given study, 100 users are randomly surveyed. X is the count of the number of survey respondents who live outside of the United States. Find the mean of X. Round this and subsequent answers to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
b) Find the variance of X. |
Algebraic Expression:
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Hints: |
variance = 100*0.7*0.3 Answer: 21 |
C)
c) Find the standard deviation of X. Answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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D)
Using the normal approximation to the binomial, calculate P(X≤65). Round decimal answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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21) Problem #PRAEVSZ "PRAEVSZ - 136949 - You win a game if..." |
A)
You win a game if you roll a die and get a 2 or a 5. You play this game 60 times. a) What is the probability that you win between 13 and 19 times (inclusive)? Round this and subsequent answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
b) What is the probability that you will win the game
at least 15 times? |
Algebraic Expression:
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C)
c) What is the probability that you will win the game fewer than 21 times? |
Algebraic Expression:
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Hints: |
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D)
d) What is the most likely number of wins. |
Algebraic Expression:
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E)
e) What is the probability of obtaining the number of wins in d? |
Algebraic Expression:
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F)
Can we use the normal approximation to the binomial? In other words, are n*p≥10 and n*q≥10? |
Multiple Choice:
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G)
What is the standard deviation of X, the count of wins? Round answer to the nearest hundredth. |
Algebraic Expression:
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H)
Using the normal approximation to the binomial, find P(X≤16). Round answer to the nearest hundredth. |
Algebraic Expression:
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22) Problem #PRAEX9U "PRAEX9U - 139331 - You are to take a..." |
A)
You are to take a multiple choice exam consisting of 100 questions with five possible responses to each. Suppose you did not study and decided to guess randomly on each question. Let X = the number of correct answers. Find the probability that you score less than a 16 or at least a 22. Answer this question and subsequent questions by rounding answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
b) Find the probability you scored at most 18 or more than 24. |
Algebraic Expression:
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C)
c) Find the probability you score at least 19. |
Algebraic Expression:
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D)
d) Find the mean of X. |
Algebraic Expression:
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E)
e) Find the standard deviation of X. |
Algebraic Expression:
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F)
f) What assumptions need to be checked if we are going to use the normal approximation to the binomial? a) n*p≥10 only b) n*q≥10 only c) n*p≥10 and n*q≥10 d) n*p≤10 and n*q≤10 e) n*p≥5 and n*q≥5 f) No assumptions need to be checked - the binomial can always be approximated using the normal distribution. |
Multiple Choice:
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G)
g) Can we use the normal approximation to the binomial for the problem pertaining to guessing on the multiple choice exam? |
Algebraic Expression:
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H)
h) Using the normal approximation to the binomial, approximate the P(X≥22). |
Algebraic Expression:
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I)
i) Using the normal approximation ot the binomial, find P(X≤15). |
Algebraic Expression:
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23) Problem #PRAEX9W "PRAEX9W - 139333 - The Geometric Dis..." |
A)
The Geometric Distribution has the same setting as the binomial: 1) Two outcomes called "success" or "failure". 2) All observations are independent. 3) The probability of "success", p, is constant. However, for the binomial the random variable X is the count of successes in n trials. For the Geometric Distribution, X is the number of trials required to obtain the first success. Overview of the Geometric Distribution: Calculating Geometric Probabilities: P(X=x) = (qx-1)*p Mean or Expected Value of X: E(X) = μx = 1/p Variance of X: VAR(X) = σ2 = q/p2 Calculating "more than" problems - The probability that it takes more than x trials to see the first success is: P(X > x) = qx Question: Suppose 20% of the cereal boxes contain a prize. You are determined to buy cereal boxes until you win a prize. What is the probability that you will win on your second box? © STATS4STEM.ORG |
Algebraic Expression:
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B)
b) How many boxes are you expected to buy before you win? |
Algebraic Expression:
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C)
c) What is the variance of X? |
Algebraic Expression:
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Hints: |
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D)
d) What is the probability your first win comes on your 8th purchase? Round answer to the nearest hundred. |
Algebraic Expression:
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Hints: |
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E)
e) What is the probability that it will take more than 5 purchases to win? Round to the nearest hundred. |
Algebraic Expression:
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Hints: |
Calculating "more than" problems - The probability that it takes more than x trials to see the first success is: P(X > x) = qx |
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F)
f) Is the Geometric Distribution a discrete or continuous distribution? |
Multiple Choice:
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G)
g) Calculate the probability that you will have to buy at most two boxes. Round to the nearest hundred. |
Algebraic Expression:
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H)
h) What is the probability that you will have to buy less than 6 boxes to win your first prize? Round to the nearest hundred. |
Algebraic Expression:
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Hints: |
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24) Problem #PRAEX96 "PRAEX96 - 139341 - Three friends eac..." |
A)
Three friends each toss a coin. The odd man wins; that is, if one coin comes up different from the other two, that person wins that round. For example, if the outcome was HHT, the friend with the tails is the one who wins. If the coins all match, then no one wins and they toss again. We're interested in the number of times the players will have to toss the coins until someone wins. a) What is the probability that no one will win? For this problem and subsequent problems, round answers to the hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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Therefore, P(HHH or TTT) = P(HHH) + P(TTT) - P(HHH and TTT) = .125 + .125 - 0 ( HHH and TTT are DISJOINT or mutually exclusive events ... they can't happen at the same time) |
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B)
b) Define a success as "someone wins on a given coin toss." What is the probability of a success. Round answer to the nearest hundred. |
Algebraic Expression:
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Hints: |
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Answer = 0.75 |
C)
c) Lets define a random variable of interest: X = number of games until someone wins. Construct a probability distribution table for X (Your first row is, X, your outcomes. Only list 1 through 4 (inclusive)). Your second row should be P(X=x). Then extend your table by the addition of cumulate probabilities in a third row. |
Multiple Choice:
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D)
d) What is the probability that it takes no more than 3 rounds for someone to win? Round answer to nearest hundred. |
Algebraic Expression:
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Hints: |
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E)
e) What is the probability that it takes at most 2 rounds for someone to win? Round answer to nearest hundred. |
Algebraic Expression:
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Hints: |
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25) Problem #PRAJBZG "PRAJBZG - 239977 - 20% of the popula..." |
A)
20% of the population have green eyes. Individuals are randomly sampled from the population, one-by-one. X represents the number of individuals sampled to find the first person with green eyes. What type of distribution is this? © STATS4STEM.ORG |
Multiple Choice:
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B)
What is the expected value of X? Round answer to the nearest hundredth. |
Exact Match (case sensitive):
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Hints: |
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Answer = 5 |
C)
What is the probability that the first person to have green eyes comes on the 9th sample? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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Answer = 0.03 (ROUNDED) |
26) Problem #PRAJBZW "PRAJBZW - 239990 - You decide that y..." |
A)
You decide that you want to find out the average annual income of small businesses in your city. You choose a SRS of 200 small businesses to call. For each small business you contact, there is a 63% chance that you will receive a response. Assume that the 63% response rate is constant across all types of small businesses. ______________________________________________________ Is this a binomial setting? |
Multiple Choice:
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Hints: |
1) Two outcomes: success or failure 2) There is fixed number of trials 3) The outcomes of each trial are independent of each other 4) The probability of a success remains the same for each trial |
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B)
What is the number of small businesses that are expected to respond? |
Algebraic Expression:
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Hints: |
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p = 0.63 |
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C)
What is the probability that more than 111 small businesses will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R/Rweb: P(X≤x) = pbinom(x, n, p) |
binomcdf(200,0.63,111)
Enter in R/Rweb:
pbinom(111,200, 0.63) |
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D)
What is the probability that exactly 134 small businesses will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X=x) = binompdf(n,p,x) R/Rweb: P(X=x) = dbinom(x, n, p) |
binompdf(200,0.63,134) Enter in R/Rweb: dbinom(134,200, 0.63) |
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E)
What is the probability that at least 120 small businesses will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R/Rweb: P(X≤x) = pbinom(x, n, p) |
binomcdf(200,0.63,119) Enter in R/Rweb:
pbinom(119,200, 0.63) |
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27) Problem #PRAJBY6 "PRAJBY6 - 239967 - Helga plays a gam..." |
Helga plays a game where she wins on average once every 8 games. Let X be the number of games she must play until she wins. What is the standard deviation of X? Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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28) Problem #PRAJBY7 "PRAJBY7 - 239968 - X ~ B (12, 0.75)...." |
X ~ B (12, 0.75). Find the P(X > 5). Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R/Rweb: P(X≤x) = pbinom(x, n, p) |
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29) Problem #PRAJBYW "PRAJBYW - 239959 - X ~ B (12, 0.75)...." |
X ~ B (12, 0.75). Using the Binomial Distribution formula, find the P(X = 7). Round answer to the nearest hundredths.
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Algebraic Expression:
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Hints: |
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30) Problem #PRAJBYX "PRAJBYX - 239960 - X ~ B(12 , 0.75)...." |
X ~ B(12 , 0.75). Find the P(X < 8). Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R/Rweb: P(X≤x) = pbinom(x, n, p) |
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31) Problem #PRAJH4T "PRAJH4T - 245846 - In a binomial dis..." |
A)
In a binomial distribution, are the variables continuous or discrete? © STATS4STEM.ORG |
Multiple Choice:
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B)
True or false. In a binomial distribution, each of the trials must be independent of each other. |
Multiple Choice:
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C)
True or false. The probability of success does not have to be constant from trial to trial. |
Multiple Choice:
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D)
Which of the following is NOT a good example of a scenario in which a binomial distribution could be used? |
Multiple Choice:
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Hints: |
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E)
True or false. In a binomial distribution there must be a fixed number of trials |
Algebraic Expression:
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F)
If there is a problem on the number of defects in a lot of goods if the machine is adjusted, is that a good scenario for a binomial distribution? |
Multiple Choice:
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Hints: |
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32) Problem #PRAJH4V "PRAJH4V - 245848 - Dana is an 83% fr..." |
Dana is an 83% free-throw shooter. What is the probability that his first success is on the third try? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
The equation is: P(x=n) = qn-1 x p Where q = .17, n = 3, and p = .83 |
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33) Problem #PRAJH4W "PRAJH4W - 245849 - Harry scores goal..." |
Harry scores goals 66% of the time he tries to score in soccer. What is the probability that it takes him more than 2 kicks at the goal to score? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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34) Problem #PRAJBZ3 "PRAJBZ3 - 239995 - What is 10 choose..." |
What is 10 choose 6? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
6!(10-6)! |
6x5x4x3x2x1x4x3x2x1 |
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35) Problem #PRAJBZ5 "PRAJBZ5 - 239997 - X~B(10,.2). Round..." |
A)
X~B(10,.2). Round all your answers to the nearest hundreth. a. Find P(X=2) © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
b. Find the Mean |
Algebraic Expression:
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Hints: |
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C)
c. Find the Standard Deviation |
Algebraic Expression:
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Hints: |
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36) Problem #PRAJBZQ "PRAJBZQ - 239984 - There are 30 stud..." |
There are 30 students in a math class. 75% of the students completed their homework. If the teacher randomly checks 20 students’ homework, what is the probability that at least 15 of them completed the homework assignment? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Number:
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Hints: |
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p = 0.75 |
binomcdf(20,0.75,14) |
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37) Problem #PRAJBZR "PRAJBZR - 239985 - You flip a fair c..." |
You flip a fair coin 25 times. What is the probability of getting no more than 11 heads? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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binomcdf(25,0.5,11) |
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38) Problem #PRAJBZS "PRAJBZS - 239986 - You flip a fair c..." |
You flip a fair coin 25 times. What is the probability of getting exactly 14 tails? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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binompdf(25,0.5,14) |
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39) Problem #PRAJBY8 "PRAJBY8 - 239969 - Each child born t..." |
Each child born to a particular set of parents has probability 0.15 of being blind. If the parents had 8 children, what is the probability that exactly 2 are blind? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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40) Problem #PRAJQUZ "PRAJQUZ - 251370 - A group of 30 chi..." |
A)
A group of 30 children took a test and the probability of passing is .70. What is the probability that exactly 25 passed? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
What is the probability that at least 26 children passed? |
Algebraic Expression:
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Hints: |
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41) Problem #PRAJQU7 "PRAJQU7 - 251376 - Buying a used car..." |
Buying a used car for a good price is not always a guaranteed outcome. Usually there is a heavy amount of bargaining. The probability that Bob achieves success (buys a car for a good price) is .34. What is the probability that he achieves his first success on the 4th sales meeting? Round answer to the nearest thousandths. © STATS4STEM.ORG |
Multiple Choice:
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42) Problem #PRAJQU8 "PRAJQU8 - 251377 - Williams College ..." |
Williams College located in Williamstown, MA is currently ranked the number one liberal arts college in America. They only accept 20 percent of their applicants. The admissions committee begins to review applications in a random order. What is the probability that the committee's first application chosen for addmission is the third application that is reviewed? Round answer to the nearest hundredths. © STATS4STEM.ORG |
Multiple Choice:
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43) Problem #PRAJQU9 "PRAJQU9 - 251378 - Tufts University ..." |
Tufts University in Medford is a very prestiguous school in Massachusetts and for the past 2 years at Boston Latin School 160 students applied there. Only 42 got accepted. that means that the probability of obtaining an acceptance is .263. What is the probability that a student gets their first success (an acceptance) on the second try? (This scenario implies that a student has applied and been rejected the first time.) Round answer to the nearest thousandths. ???? © STATS4STEM.ORG |
Multiple Choice:
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44) Problem #PRAJQVA "PRAJQVA - 251379 - For high school s..." |
A)
For high school seniors, prom season is fast approaching. Tommy needs to find a date soon and he has a .25 chance of success. Assume that this percentage is constant for all girls that he plans to ask. What is the probability that he gets his first success (a yes) on the third girl he asks? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
Tommy is really striking out because he waited too long to ask somebody to prom. What is the probability that the 5th girl will say yes? |
Algebraic Expression:
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45) Problem #PRAJBZN "PRAJBZN - 239982 - You are shooting ..." |
A)
You are shooting free throws at basketball practice. The chance that you make the shot is 0.6 or 60%. What is the probability that you will make your first shot? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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p = 0.6 q = 0.4 |
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B)
What is the probability that it will take you more than two shots to make one? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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n = 2 |
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46) Problem #PRAJBZJ "PRAJBZJ - 239979 - A DVD player comp..." |
A)
A DVD player company made 100 machines and each machine has a 8.5% probability of not functioning properly. Find the probability that 7 wont function properly. Round answer to the nearest hundredths. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
Find the probability that 11 don't work properly. (round to the nearest hundredths place) |
Algebraic Expression:
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Hints: |
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C)
Find the probability that more than 6 won't function properly. (round to the nearest hundredths place) |
Algebraic Expression:
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Hints: |
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1-binomcdf(100, 0.085, 6) |
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47) Problem #PRAJBZP "PRAJBZP - 239983 - You have a bag of..." |
A)
You have a bag of 10 marbles. 4 marbles are red, 4 marbles are blue, and 2 marbles are green. You close your eyes and pick one marble from the bag. You replace the marble after each trial so that the chance of choosing a certain marble remains constant. ________________________________________________________ |
Algebraic Expression:
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Hints: |
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B)
If a success is defined as choosing a red marble, what is q? |
Algebraic Expression:
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Hints: |
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C)
If a success is defined as choosing a red marble, what is the probability that your first success occurs on your fourth attempt? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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q = 0.6 n = 4 |
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D)
If a success is defined as choosing a red marble, what is the probability that it will take you more than four attempts to choose a red marble? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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n = 4 |
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48) Problem #PRAJBZH "PRAJBZH - 239978 - Toyota found that..." |
A)
Toyota found that 47% of their brakes had problems from their new production of 1.5 million cars. They decided to test 95 of their products to see if they will have brake failure. What is the probability that 56 will have brake failure. Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
P(X = x) = binompdf(n, p, x) |
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B)
Find the probability that less than 38 or more than 52 cars will have a brake failure. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
P(X ≤ x) = binomcdf(n, p, x) |
P(A or B) = P(A) + P(B) |
P("less than 38") = P(X ≤ 37) = binomcdf(95, 0.47, 37) P("more than 52") = 1 - P(X ≤ 52) = 1 - binomcdf(95, 0.47, 52) |
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49) Problem #PRAJ733 "PRAJ733 - 266004 - There are 15 card..." |
A)
There are 15 cards in a pile. 5 are hearts, 6 are spades, and 4 are diamonds. You close your eyes and pick one card from the deck. You replace the card after each trial so that the chance of choosing a certain card remains constant. ________________________________________________________ |
Algebraic Expression:
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Hints: |
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B)
If a success is defined as choosing a card which is a diamond, what is q? |
Algebraic Expression:
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Hints: |
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C)
If a success is defined as choosing a card which is a heart, what is the probability that your first success occurs on your second trial? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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q = 0.67 n = 2 |
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D)
If a success is defined as choosing a card which is a diamond, what is the probability that it will take you more than two attempts to choose a card which is a diamond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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n = 2 |
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50) Problem #PRAJ85P "PRAJ85P - 267015 - Your statistics t..." |
A)
Your statistics teacher wants you to work on a project that finds out the average number of hours of sleep a student gets on a school night. You choose a SRS of 100 students to ask. For each student you ask, there is a 87% chance that you will receive a response. Assume that the 87% response rate is constant for all the students. ______________________________________________________ Is this a binomial setting? © STATS4STEM.ORG |
Multiple Choice:
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Hints: |
1) Two outcomes: success or failure 2) There is fixed number of trials 3) The outcomes of each trial are independent of each other 4) The probability of a success remains the same for each trial |
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B)
What is the number of students that are expected to respond? |
Algebraic Expression:
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Hints: |
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p = 0.87 |
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C)
What is the probability that more than 90 students will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R or R-Web P(X≤x) = pbinom(x, n, p) |
binomcdf(100,0.87,90)
Enter in R/Rweb:
pbinom(90,100,0.87) |
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D)
What is the probability that exactly 84 students will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X=x) = binompdf(n,p,x) R or RWeb P(X=x) = dbinom(x, n, p) |
binompdf(100,0.87,84) Enter in R/Rweb: dbinom(84,100,0.87) |
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E)
What is the probability that at least 79 students will respond? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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P(X≤x) = binomcdf(n,p,x) R or Rweb P(X≤x) = pbinom(x, n, p) |
binomcdf(100,0.87,78) Enter in R/Rweb:
pbinom(78,100,0.87) |
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51) Problem #PRAJBYU "PRAJBYU - 239957 - Agatha is a high ..." |
Agatha is a high school basketball player. The probability of her making a free throw is 65%. What is the probability that Agatha makes her first free throw on her fourth shot? Round answer to the nearest hundredths place. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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52) Problem #PRAJBYZ "PRAJBYZ - 239962 - You play a game w..." |
A)
You play a game where you have to roll a fair six-sided die. If your die lands on a 3 or a 6, you win a prize. What is the probability of winning for the first time on the third try? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
What is the probability that it will take more than 7 tosses for someone to win? Round your answer to the nearest hundredths place. |
Algebraic Expression:
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Hints: |
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C)
What is the probability that it will take no more than 8 tosses for someone to win? Round your answer to the nearest hundredths place. |
Algebraic Expression:
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Hints: |
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D)
What is the expected number of tosses needed for someone to win? |
Algebraic Expression:
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Hints: |
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53) Problem #PRAP57Q "PRAP57Q - Problem #383359" |
A)
Mr. Smith gives a pop quiz in his statistics class with just two questions. He gives no partial credit. X is a random variable that represents the number correct on any given quiz. For this quiz, the distribution of X is:
Find the mean of X. |
Algebraic Expression:
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Hints: |
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Answer = 1.5 |
B)
Calculate the standard deviation of X. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
Remember, to find the standard deviation, take the square root of the calculated variance. |
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C)
The teacher randomly inspects 10 quizzes, what is the probability that exactly 2 tests have all questions wrong? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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TI-CALC => binompdf(10, 0.1, 2) R/Rweb => dbinom(2, 10, .1) |
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D)
The teacher then decides to randomly look through the quizzes until she finds a quiz with exactly 1 wrong. What is the probability that she finds such a quiz on the 3rd quiz she looks looks at? Rouund answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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Answer = 0.15 (ROUNDED) |
54) Problem #PRAP9H9 "PRAP9H9 - Problem #386569" |
A)
A student takes a history quiz composed of 10 multiple choice questions. There are 27 students in the students class. Due to the fact that the student studied all night for his statistics course, the student is completely unprepared for the history quiz and guesses on all the questions. Each question on the quiz has 4 possible answers (a,b,c, or d). After the quiz is over, the student decides to calculate the probability that he gets exactly 3 questions correct. He decides to use the following binomial formula. For this problem, what is p in the formula below? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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p = 0.25 |
B)
For this problem, what is n for the formula above? |
Algebraic Expression:
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Hints: |
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C)
For this problem, what is k for the formula above? |
Algebraic Expression:
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Hints: |
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D)
By hand, please calculate "10 choose 3". |
Algebraic Expression:
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Hints: |
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Thus, 10 choose 3 = 120 |
E)
Calculate the probability that the student gets exactly 3 questions correct. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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