Question

Audi and VW Auto Clinic 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
monthly services cost are approximately normally distributed, with a mean of R150.00 and a standard
deviation of R25.00.
a) If the company offers the service contract to customers for a monthly charge of R200.00, what is the
probability that any one customer’s service costs will exceed the contract price of R200.00? (5)
b) What is the company’s expected profit per service contract?

Answer 1

Audi and VW Auto Clinic 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
monthly services cost are approximately normally distributed, with a mean of R150.00 and a standard
deviation of R25.00.
a) If the company offers the service contract to customers for a monthly charge of R200.00, what is the
probability that any one customer’s service costs will exceed the contract price of R200.00? (5)

z = (x-µ)/σ

z value for 200, z=(200-150)/25 = 2

P( x > 200) = P( z > 2) = 0.0228

The required probability = 0.0228

Excel function used: =1-NORM.S.DIST(2,TRUE)

b) What is the company’s expected profit per service contract?

company’s expected profit = 150*0.0228=3.42

=R3.42