Each day hundreds of deliveries are scheduled.

Each day hundreds of deliveries are scheduled. The manager decides to monitor the time deviations by taking a random sample of 16 deliveries and calculating the average deviation defined by D = 1/16 Di i=1 16 ∑ for each day. Assume that historical data such as that displayed in part (1) suggests that the distribution of deviations Di have a mean of 27 minutes and a standard deviation of 20 minutes. Find the probability that the sample mean is less than 15 minutes. (i.e. Find P[ D < 15] for a sample of size n=16)