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.
a. A random sample of n = 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 = 100? Explain.
c. Suppose that the sample size is n = 200 rather than n = 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 = 200? Explain.
e. When n = 200, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10?