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QUESTION 3 a) b) The queuing time, X minutes, of a customer at a supermarket has probability density function of a continuous random variable and is given by 3 x{k-x). ID 51:5 in: _ 32 x} _ D, othenvlse i. Show that the value of k is it. {3 marks] ii. Calculate the mean of queuing time in minutes. {2 marks] iii. Find the standard deviation of queuing time in minutes {3 marks] The time for a mail carrier to cover a route is normally distributed with average 3i) minutes and a variance of 64 minutes. If one of these trips is selected at random, i. Find the probability that a randome selected carrier will have more than 21 minutes route time. {3 marks] ii. Eighty percent of the users are said to spend at most 36 minutes en route. Assume that the mean remains the same. but the standard deviation has changed. Find the value of the new standard deviation. {4 marks)