Radio Shack stocks four alarm clock radios. If it has fewer than four clock radios available at the end of a week, the store restocks the item to bring the in-stock level up to four. If weekly demand is greater than the four units in stock, the store loses the sale. The radio sells for $25 and costs the store $15. The Radio Shack manager estimates that the probability distribution of weekly demand for the radio is as follows:
x (Weekly Demand) P(x)
0…………………………………….0.05
1…………………………………….0.05
2…………………………………….0.10
3…………………………………….0.20
4…………………………………….0.40
5…………………………………….0.10
6…………………………………….0.05
7…………………………………….0.05
a. What is the expected weekly demand for the alarm clock radio?
b. What is the probability that weekly demand will be greater than the number of available radios?
c. What is the expected weekly profit from the sale of the alarm clock radio? (Remember: There are only four clock radios available in any week to meet demand.)
d. On average, how much profit is lost each week because the radio is not available when demanded?