What is the probability that the technician can fix ten air conditioners in less than twelve hours?

Question

A technician can service an air conditioner in an average of one hour and fifteen minutes with a standard deviation of 20 minutes. (Assume the time is normally distributed). What is the probability that the technician can fix ten air conditioners in less than twelve hours?

Answer 1

10 a/c in less than 12 hours is same as 1 a/c in less than 1.2 hours. Average is 1.25 hours (1 hour 15 minutes) and SD is 0.333 hours (20 minutes)

let x = hours

z = (x - mean)/SD = (x - 1.25)/0.333

P(x < 1.2) = (z < (1.2-1.25)/0.333) = P(z < -0.15) = 0.4404