8.28 The article “Should Pregnant Women Move? Linking Risks for Birth Defects with Proximity to Toxic Waste Sites” (Chance [1992]: 40– 45) reported that in a large study carried out in the state of New York, approximately 30% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that p 5 .3.

a. Would p⁄

based on a random sample of only 10 residents have approximately a normal distribution?

Explain why or why not.

b. What are the mean value and standard deviation of p⁄

based on a random sample of size 400?

c. When n 5 400, what is P(.25 # p⁄

# .35)? (Hint:

See Example 8.9.)

d. Is the probability calculated in Part

(c) larger or smaller than would be the case if n 5 500?

Answer without actually calculating this probability.