8.25 ▼ The article “Unmarried Couples More Likely to Be Interracial”

(San Luis Obispo Tribune, March 13, 2002) reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.
(Hint: See Example 8.9.)

a. A random sample of n 5 100 couples will be selected from this population and p⁄
, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of p⁄
?

b. Is it reasonable to assume that the sampling distribution of p⁄
is approximately normal for random samples of size n 5 100? Explain.

c. Suppose that the sample size is n 5 200 rather than n 5 100, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p⁄
? If so, what are the new values for the mean and standard deviation? If not, explain why not.

d. Is it reasonable to assume that the sampling distribution of p⁄
is approximately normal for random samples of size n 5 200? Explain.

e. When n 5 200, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10?