3. (a) The heights of 1000 students are approximately normally distributed with a mean of 62.3 inches and a standard deviation of 2.4 inches. i. A student is selected randomly from the population. Find the probability that his height falls between between 60.5 and 63.5 inches inclusively. (4 marks) ii. If 200 random samples of size 20 are drawn from this population and the mean of heights of each sample is recorded, estimate the number of sample means that fall between 61.2 and 63.2 inches inclusively. (6 marks) (b) A survey is conducted about the election of the mayor of City A. It follows from the historical records that the probability that a citizen will vote on the Election Day is 0.48. Now 200 citizens are selected randomly, what is the probability that at least 50% of them will vote on the Election Day? State any assumption(s) /approximation(s) used. (5 marks) (c) There are 4 honeymoon suites in a luxury hotel. The demand of the honeymoon suites follows a Poisson distribution with a mean of 3 suites per day. i. Find the probability that the demand of the honeymoon suites is satisfied on a randomly selected day. (4 marks) ii. Given that the demand of the honeymoon suites of the hotel is at least 2 in a randomly selected day, what is the probability that the hotel can satisfy the demand in that day? (6 marks)