Question

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 9 hours.

a. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 ​hours? ​P(70less than or equalsx overbarless than or equals80​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

Given

=75

= 9

Now calculate p(70 < x < 80)

P(70 < x < 80) = p(x-/ < z < 0) + p(0 < x < x-/)

= (80-75/9 < z < 0) + p(0 < z < 70-75/9)

= (0.56 < z < 0) + p(0 < z < -0.56)

= 0.2123 + 0.2123

P(70 < x < 80) = 0.4246