2. Let's assume for the moment that the true population average number of hours worked last week for 18-64 year olds in the United States is ,u, = 30 and that the variance of the number of hours worked last week for this population is a2 = 121 hours squared. Suppose that you decide to conduct a simple random sample of 169 18-64 year olds living in the United States. (a) Using the normal approximation for the distribution of the sample average, what is the probability of obtaining a value of X greater than 31 hours? (b) Using the normal approximation for the distribution of the sample average, what is the probability of obtaining a value of X more than 1 hour away from the true population mean of 30 hours? In other words, was is the pvalue for 31 hours? (c) Is X = 31 in the 95% acceptance interval? How can you tell? (d) Under what circumstances is it appropriate to use the normal approximation for the distribution of the sample average