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 se-
lected from this population and p, the proportion of
couples that are mixed racially or ethnically, will be
computed. What are the mean and standard devia-
tion of the sampling distribution of ?
b. Is it reasonable to assume that the sampling distribu-
tion of p is approximately normal for random sam-
ples 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 distribu-
tion of p is approximately normal for random sam-
ples 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?