Question

The time required for Quick Changers to complete an oil change service on an automobile follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. Quick Changers guarantees customers that the service will take no longer than 20 minutes, else the service is half-price.

If Quick Changers does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit? (Round to the nearest minute.) Hint: You want the area in the right tail to be 3%. If that's the case, how much area is to the left of the time value you're looking for?)

Answer 1

mean μ=	17.000
standard deviation σ=	2.500

as top 3% will fall at 97th percentile:

for 97th percentile critical value of z=		1.88
therefore corresponding value=mean+z*std deviation=			21.70 minutes