would the graph for this have a left or right tail: Answer: Answer: (a) The probability that exactly 25 students are more likely to re-enroll is approximately 0.159. (b) The probability that at least 30 students are more likely to re-enroll is approximately 0.047. (c) The probability that at most 24 students are more likely to re-enroll is approximately 0.689. Explanation: First, we need to check if we can use a normal distribution to approximate the binomial distribution. The rule of thumb is that we can do this if both np and n(1-p) are greater than or equal to 5, where n is the number of trials (in this case, the number of students surveyed) and p is the probability of success (in this case, the probability that a student is more likely to re-enroll). Here, np = 40 * 0.62 = 24.8 and n(1-p) = 40 * 0.38 = 15.2, both of which are greater than 5. So, we can use a normal distribution. Next, we find the mean and standard deviation of the normal distribution. The mean is np = 24.8 and the standard deviation is sqrt(np(1-p)) = sqrt(24.8 * 0.38) = 2.73. (a) To find the probability that exactly 25 students are more likely to re-enroll, we need to find the z-score for 25, which is (25 - 24.8) / 2.73 = 0.07. The probability corresponding to this z-score is approximately 0.159. (b) To find the probability that at least 30 students are more likely to re-enroll, we need to find the z-score for 30, which is (30 - 24.8) / 2.73 = 1.91. The probability corresponding to this z-score is