Question 2 [10 marks] In a recent study at the University of Southern California Schaeffer Center for Health Policy and Economics, researchers concluded that customers overpaid for prescriptions 23% of the time. This overpayment often occurs because the copay is higher than the full cost of a drug. Suppose four prescriptions are selected at random. Let X be a random variable defined to be the number of prescriptions for which the customer overpaid. a. [5 marks] Find the probability distribution for X. Round to four decimal places. Show all your work. b. [3 marks] Find the mean, variance, and standard deviation of X. c. [2 marks] Suppose all four customers overpaid for their prescriptions. Is there any evidence to suggest that the percentage reported in this study is wrong? Justify your