Defective items in a batch. A manufacturer sells his products in boxes containing 50 items. He claims that on an average, a box will contain no more than four defective items.

In order to verify his claim, a box is selected randomly and its items checked. It has been found that the box contains eight defective items. Assume that the standard deviation of the number of defective items per box is 1.5.

a. If the mean number of defectives per box is really 4 what is the z-score corresponding to eight?

b. Considering your answer to part

a, do you have any reason to believe that the manufacturer’s claim is correct?

c. What would be your answer if the standard deviation is assumed to be 1.25 instead of 1.5?