The tread life of a particular brand of tire is a random var

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2700 miles. What is the probability a particular tire of this brand will last longer than 57,300 miles?

a. .2266

b. .8413

c. .7266

d. .1587

Solution

MEAN = 60000

STD DEV = 2700

P(X>57300) =

For x = 57300, z = (57300 - 60000) / 2700 = -1

Hence P(x > 57300) = P(z > -1) = [total area] - [area to the left of -1]

= 1 - 0.1587 = 0.8413