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. What percent of customers receive the service for half-price? (Write your answer as a percent, rounded to the nearest tenth of a percent.)

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

Solution :

Given that ,

mean = = 17

standard deviation = = 2.5

a) P(x < 20) = P[(x - ) / < (20 - 17) / 2.5]

= P(z < 1.2)

Using z table,

=0.8849

The percentage is = 88.49%

b) Using standard normal table,

P(Z < z) = 3%

= P(Z < z) = 0.03  

= P(Z < -1.88 ) = 0.03

z = -1.88

Using z-score formula,

x = z * +

x = -1.88 * 2.5 + 17

x = 12.3

d it make the guaranteed time limit = 12 minutes