Let X denote the amount of time a randomly selected customer spends in a retail store. Suppose X follows a distribution with a mean of 10 minutes and a standard deviation of 6 minutes. Its density curve is given below. Population Distribution for Time Spent in Store 5 10 15 20 25 30 Time Spent in Store (min) Online STAT l5l Total: 102 marks a) Describe the shape of the population distributionlz marks) b) If you randomly pick nine customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape. {3 marks] c) If you randomly pick 36 customers, describe the sampling distribution of the average time spent in the store; provide the mean, standard deviation, and shape. {3 marks) d) If you randomly pick 36 customers, find the probability that the average time spent in the retail store is at least 11.5 minutes. {4 marks)