Ward Doering Auto Sales is considering offering a special service contract that will cover the total cost of any service work required on leased vehicles. From experience, the company manager estimates that yearly service costs are approximately normally distributed, with a mean of $150 and a standard deviation of $25. a. If the company offers the service contract to customers for a yearly charge of $200, what is the probability that any one customer’s service costs will exceed the contract price of $200?

b. What is Ward’s expected profit per service contract?

a. The probability that any one customers service costs will exceed the contract price of $200 is 0.0228

b. Warda expected profit per service contract is $50

Explanation:

a. In order to calculate  the probability that any one customers service costs will exceed the contract price of $200 we would have to calculate first the z value as follows:

z=x-μ/σ

z=$200-$150/$25

z=2

Therefore, probability that any one customers service costs will exceed the contract price of $200 is p(x>$200)=p(z>2)

=1-p(z≤2)

=1-0.9772

=0.0228

The probability that any one customers service costs will exceed the contract price of $200 is 0.0228

b. To calculate Warda expected profit per service contract we would have to make the following calculation:

Warda expected profit per service contract=service charge per contract-expected cost

Warda expected profit per service contract=$200-$150

Warda expected profit per service contract=$50

Warda expected profit per service contract is $50