An article reported that 7% of married couples in the UnitedStates are mixed racially or ethnically. Consider the populationconsisting of all married couples in the United States.
(a) A random sample of n = 50 couples will be selectedfrom this population and p?, the proportion of couplesthat are mixed racially or ethnically, will be computed. What arethe mean and standard deviation of the sampling distribution ofp?? (Round your standard deviation to four decimalplaces.)
(b) Is it reasonable to assume that the sampling distribution ofp? is approximately normal for random samples of sizen = 50? Explain.
Yes, because np < 10 and n(1 ?p) < 10. Yes, because np > 10 andn(1 ? p) > 10. No,because np < 10. No, because np > 10.
(c) Suppose that the sample size is n = 250 rather thann = 50, as in Part (b). Does the change in sample sizechange the mean and standard deviation of the sampling distributionof p?? What are the values for the mean and standarddeviation when n = 250? (Round your standard deviation tofour decimal places.)
(d) Is it reasonable to assume that the sampling distribution ofp? is approximately normal for random samples of sizen = 250? Explain.
Yes, because np < 10. Yes, because np >10. No, because np < 10. No,because np > 10.
(e) When n = 250, what is the probability that theproportion of couples in the sample who are racially or ethnicallymixed will be greater than 0.08? (Round your answer to four decimalplaces.)
