38. Assume we know that 20% of Americans suffer from a certain type of allergy. Suppose we take a random sample of 100,000 Americans and record the percentage who suffer from this allergy. a. The Central Limit Theorem says that percentages from such surveys will be normally distributed. What is the mean of the distribution? b. What is the standard deviation of the normal distribution in part a? Round your answer to two decimal places in percentage points. c. Suppose we find that in a town of 100,000 people, 21% suffer from this allergy. Is this an unusual sample? What does the answer to such a question tell us about this town?

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38. Assume we know that 20% of Americans suffer from a certain type of allergy. Suppose
we take a random sample of 100,000 Americans and record the percentage who suffer
from this allergy.
a. The Central Limit Theorem says that percentages from such surveys will be
normally distributed. What is the mean of the distribution?
b. What is the standard deviation of the normal distribution in part a? Round your
answer to two decimal places in percentage points.
c. Suppose we find that in a town of 100,000 people, 21% suffer from this allergy. Is
this an unusual sample? What does the answer to such a question tell us about
this town?
Transcribed Image Text:38. Assume we know that 20% of Americans suffer from a certain type of allergy. Suppose we take a random sample of 100,000 Americans and record the percentage who suffer from this allergy. a. The Central Limit Theorem says that percentages from such surveys will be normally distributed. What is the mean of the distribution? b. What is the standard deviation of the normal distribution in part a? Round your answer to two decimal places in percentage points. c. Suppose we find that in a town of 100,000 people, 21% suffer from this allergy. Is this an unusual sample? What does the answer to such a question tell us about this town?
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