Cellophane that’s going to be formed into bags for items such as dried beans or bird seed is passed over a light sensor to test if the alignment is correct before it passes through the heating units that seal the edges. Small adjustments can be made by the machine automatically. But if the alignment is too bad, the process is stopped and an operator has to manually adjust it. These misalignment stops occur randomly and independently. On one line, the average number of stops is 52 per eight-hour shift.

a) What is the mean number of stops per hour?

b) What is the standard deviation of stops per hour?

c) When the machine is restarted after a stop, what is the probability that it will run at least 15 minutes before the next stop?