An article reported that 4% 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 13, 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 13? (Round your standard deviation to four decimal places.) mean 0.04 v : standard deviation 0.0196 v (b) Is it reasonable to assume that the sampling distribution off) is approximately normal for random samples of size n = 100? Explain. Yes, because np 10 and n(1 p) > 10. No, because np 10. u! (c) Suppose that the sample size is n = 300 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? What are the values for the mean and standard deviation when n = 300? (Round your standard deviation to four decimal places.) mean 0.04 v standard deviation 0.0113 (d) Is it reasonable to assume that the sampling distribution off) is approximately normal for random samples of size n = 300? Explain. , Yes, because np 10. No, because np 10. V (e) when n = 300, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.05? (Round your answer to four decimal places.)