Question

4. The life span of a machined part produced follows a normal distribution. It has a mean of 1525 hours and a standard deviation of 60.5 hours. What is the probability that a part will have a life span: a) exceeding 1600 hours? b) between 1450 and 1650 hours?

Answer 1

4.

A.

Z = (1600-1525)/60.5

Z = 1.24

At this value of Z, area covered = .8925

So,

Probability to exceed 1600 hours = 1-.8925

Probability to exceed 1600 hours = .1075 or 10.75%

B.

First calculation: Probability of less than 1450 hours

Z = (1450-1600)/60.5 = -2.48

Area covered at this value of Z = .0066

Second calculation: Probability of less than 1650 hours

Z = (1650-1600)/60.5 = .83

Area covered at this value of Z = .7967

So,

Area covered for between 1450 and 1650 hours = .7967 - .0066 = .7901 or 79.01%

Required probability for life in between 1450 and 1650 hours = .7901 or 79.01%