Question

A plant manufacturers 12 voltage DC Power Supplies. Two engineers, Kelsier and Dockson, are given access to a batch of 500 power supplies to test. Their tests determine the maximum power that the power supply can provide for a sustained period of time. Kelsier, a newly hired quality control engineer randomly selects 10 power supplies from this batch, and his tests results in a sample mean of 150.030 W and the sample standard deviation of 3.502 W. Dockson, another quality control engineer has worked for the company for a long time, and knows from past experience that the average capacity of the power supplies that they make is 151 W and sample standard deviation of 4 W. Management requires that the maximum power that the DC power supplies can provide should be at least 148 W during sustained use. Assume that the capacity of power supplies is normally distributed. a) How confident is Kelsier that the average maximum power that the average power supply of this batch can provide is at least 148 Watts? b) Based on the data provided by Dockson, estimate the number of power supplies from the given batch that do not satisfy the management requirement. List all your assumptions.