1) Problem #PRAE882 "PRAE882 - 147955 - In the United Sta..." |
A)
In the United States, about 17% of the people have blue eyes. Suppose 200 people from this city were sampled. As a decimal, what is the mean of the sampling distribution of p-hat? Source: onlinestatbook.com © STATS4STEM.ORG |
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B)
Using Rweb and the code found below, create a histogram of the sampling distribution for p-hat. x=rbinom(10000, 200, .17) p.hat=x/200 hist(p.hat, breaks=20) # construct a normal probability plot qqnorm(p.hat) qqline(p.hat) Review the histogram and the normal probability plot to assess normality. Does the sampling distribution for p-hat appear to be normal? Hint: Here is a link to review the normal probability plot. |
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C)
Review your histogram again. Use the following code if needed. x=rbinom(10000, 200, .17) p.hat=x/200 hist(p.hat, breaks=20) Using what you know about the density curve of the normal distribution, estimate the standard deviation through visual inspection of the histogram. |
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D)
What is the standard deviation of the sampling distribution of p-hat? Round answer to the nrearest thousands. |
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E)
Are the required conditions been met to use the normal approximation for p-hat? Hint: Make sure you remember these requirement and always use them before assuming normality. |
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F)
Which distribution can be used to approximate the sampling distribution of p-hat? |
Multiple Choice:
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G)
What is the probability p-hat will be less than .15? Anwer as a decimal rounded to nearest hundred. |
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z=-0.74 |
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H)
What is the probability p-hat will fall between .13 and .19? Anwer as a decimal rounded to nearest hundredth. |
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I)
What is the probability p-hat will be greater than .20? Anwer as a decimal rounded to nearest hundred. |
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P(p-hat > 0.20) = 0.1335 ANSWER = 0.13 (ROUNDED) |
J)
What is the probability p-hat will be less than .14 or greater than .18? Anwer as a decimal rounded to nearest hundred. |
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Remember, if A & B are Disjoint. P(A OR B) = P(A) + P(B) |
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2) Problem #PRAEHAB "PRAEHAB - Probability - Conditional - Two Basic Rules of Probability - CS" |
A)
Answer as a percentage rounded to the nearest whole number. Do not include % sign. |
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B)
Answer as a percentage rounded to the nearest whole number. Do not include % sign. |
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C)
Answer as a percentage rounded to the nearest whole number. Do not include % sign. |
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D)
What is the probability, as a percentage, that a member is an advanced swimmer and an intermediate swimmer? Give answer as a percentage rounded to the nearest whole number. Do not include % sign. |
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E)
Are being an advanced swimmer and an intermediate swimmer mutually exclusive or disjoint events? |
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F)
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