Question

The owners of an Italian restaurant are interested in signing a lease with a restaurant supply company for a new industrial freezer. Before deciding on the model, the owners want to get an idea of how reliable the equipment will be over the three-year term of the lease. For one particular model, the supplier informs the owners that in a given year, 80% of the freezers sold do not need service, 11% need service once, 5% need service twice, 4% need service three times, and none require service more than three times in a year.

In addition to the lease, the supplier offers a maintenance contract for unlimited repairs for a $125 fixed yearly cost and a $35 service charge for each repair required. Considering the information above to suggest a probability distribution for the number of repairs needed, use the rules of expected value to find the expected annual expense of the service contract.

Answer 1

Let X be the number of times the service (number of repairs) needed per year. The probability distribution for the number of repairs needed is,

X	P(X)
0	0.80
1	0.11
2	0.05
3	0.04

Expected number of repairs needed per year is,

E(X) = 0 * 0.80 + 1 * 0.11 + 2 * 0.05 + 3 * 0.04 = 0.33

Annual expense of the service contract = Fixed Cost + X * Service Charge

= $125 + $35 X = $ (125 + 35X)

Expected annual expense of the service contract = E(125+35X)

= 125 + 35 E(X)

= 125 + 35 * 0.33

= $136.55