A particular item is handmade in two stages by two workers f

A particular item is handmade in two stages by two workers, first by Laverne and then by Shirley. The time it takes Laverne to finish her part is normally distributed with a mean of 1.2 hours and a standard deviation of 0.3 hours. The time it takes Shirley to finish her part is normally distributed with a mean of 0.9 hours and a standard deviation of 0.2 hours. Assume the work times for Laverne and Shirley are independent of each other

(a) What is the probability that the total time it takes to make an item will be no more than 2 hours?

(b) Laverne is paid a wage of $25 per hour, and Shirley is paid a wage of $40 per hour. What is the probability that the total amount paid to the two employees to make one item will be no more than $75?

Solution