The total sleep time per night among college students was approximately Normally distributed with mean = 6.7 hours and standard deviation = 1.5 hours. You plan to take an SRS of size n= 225 and compute the average total sleep time. (10p) a. What is the standard deviation for the average time? b. What is the probability that your average will be below 6.9 hours? - Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and well approximated by the Normal distribution with mean 51.54 minutes and standard deviation 9.4 minutes. (18p) a. What is the probability that a particular delivery will exceed one hour? b. What is the probability that a particular delivery arrives in less than one hour? C. What is the probability that the mean time of five deliveries will exceed one hour?