5.37 Is the binomial distribution a reasonable approximation? In each of the following situations, is it reasonable to use a binomial distribution to approximate the sampling distribution of X? Give reasons for your answer in each case.

a. According to the Red Cross, 0.5% of the Asian ethnic group in the United States have type A–

blood.21 Suppose that this national proportion holds for your large city. If you randomly sample 500 Asian residents, can the B(500, 0.005) distribution be used for the count X of Asian residents that have type A– blood?

b. You are interested in determining the proportion of residents on the Sci Fi floor at your university who binge watch Netflix at least once a week. There are a total of 50 residents on the floor. You choose 25 residents (1 per room) at random to interview. If the true proportion is 0.80, can the B(25, 0.80) distribution be used for the count X in your sample?