Question

The time required for servicing transmissions is normally distributed with  = 45 minutes and  = 8 minutes. The service manager plans to have work begin on the transmission of a customer’s car 10 minutes after the car is dropped off and the customer is told that the car will be ready within 1 hour from drop-off. What is the probability that the service manager cannot meet his commitment?

Answer 1

Answer:0.2659

Explanation:

The work begin after 10 min, so the average time increase from 45min to 55min.

for normal distribution :-

z = (X-μ)/б

= (60-55)/8        

= 0.625

In R software for probability finding we use function called pnorm

As we want to find the probability of service manager cannot meet his commitment, So we should write below command.

1-pnorm(0.625)

=0.2659

                                                 OR

In R software we can directly write code

1-pnorm(60, mean=55, sd=8)

=0.2659