New Process Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95% of the working days. Frequent checks of the unfilled orders at the end of the day revealed that the distribution of the unfilled orders follows a Poisson distribution with a mean of two orders.
a. Has New Process Inc. lived up to its internal goal? Cite evidence.
b. Draw a histogram representing the Poisson probability distribution of unfilled orders.