Question 4 a) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4522, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the standard deviation for the probability distribution. (3 marks) b ) On a multiple-choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. (2 marks) c) A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the other. (2 marks) d) A mountain search and rescue team receive a mean of 0.53 calls per day. Find the probability on a randomly selected day, they will receive fewer than two calls. (2 marks)