Problem 1 (15 points): Suppose that probability of having at least one dental checkup during a two-year period is 65%. 40 random individuals are being studied for their health care utilization practices over a two-year period. Compute "part a" by hand and show key steps. For all other parts you may hand calculate or use R. a) What is the probability that exactly 24 of these individuals will have at least one dental checkup? b) What is the probability that at least 24 of these individuals will have at least one dental checkup? c) Could you use an approximation method to calculate the probabilities above? If yes, calculate the probabilities using approximations and compare to the exact values; otherwise, explain why approximations methods are not appropriate. d) How many individuals do you expect to have at least one dental checkup? e) What is the SD of the number of individuals who will have at least one dental checkup