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7.2 Assignment
AP Statistics
Choose an SRS of size n from a large population with population proportion p having some
characteristic of interest. Let p̂ be the proportion of the sample having that characteristic.
1. What is the mean of the sampling distribution?
2. What is the standard deviation of the sampling distribution?
3. Under what conditions can the formula for the standard deviation of p̂ be reasonably accurate?
4. The sampling distribution of p̂ is approximately normal when the sample size n is “large.”
According to our adopted rule of thumb, what conditions do we require in order to use the normal
approximation to the sampling distribution of p̂ ?
According to government data, 22% of American children under the age of 6 live in households with
incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of
300 children.
5. What is the probability that more than 20% of the sample are from poverty households?
(Remember to check that you can use the normal approximation.)
Suppose you are going to roll a fair six-sided die 60 times and record p̂ , the proportion of times that a
1 or a 2 is showing.
6. Where should the distribution of the 60 p̂ -values be centered? Justify your answer.
7. What is the standard deviation of the sampling distribution of p̂ , the proportion of all rolls of the
die that show a 1 or a 2?
8. Describe the shape of the sampling distribution of p̂ . Justify your answer.
Power companies kill trees growing near their lines to avoid power failures due to falling limbs in
storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the
chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees.
The power company tests the chemical on 250 sycamores. Consider these an SRS from the
population of all sycamore trees.
9. What are the mean and standard deviation of the proportion of trees that are killed?
10. What is the probability that at least 60 trees (24% of the sample) are killed? (Remember to check
that you can use the normal approximation.)