Question

From long term experience, it is known that the time it takes to do an oil change on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free oil change to any customer who has to wait longer than the guaranteed time it takes to complete the job.

a.) If the shop guarantees the service will take 25 minutes or less, what percentage of customers will end up receiving a free oil change?

b.) If the shop does not want to give more than 1% of its customers a free oil change, how long should the guarantee be for? (*round answer to the nearest minute*)

Answer 1

a)

The following information has been provided:

We need to compute . The corresponding z-value needed to be computed:

Therefore,

b) P[ customer waits ] = 1% = 0.01

P[ X > x ] =0.01

P[ X < ] = 1 - 0.01 = 0.99

Correspondng Z value = 2.33

X = 17.8 + 12.116

X = 29.916

X = 30 minutes