Truck tire life is normally distributed with a mean of 62302

Truck tire life is normally distributed with a mean of 62,302 miles and a standard deviation of 4,149 miles. What is the probability that a tire lasts between 54,838 and 66,843 miles?

Solution

Let X be the nomally distributed variable

Step1:
Find Z-score
Z-score = X -mean/standard deviation

Z1 = 66843 - 62302/4149 = 1.09448

Z2 = 54838 - 62302/4149 = -1.79899

step2:

P(54838< X < 66843) = P(-1.79899 < Z < 1.09448)

= P(Z < 1.09448) - P(Z < -1.79899)

= 0.8631 - 0.036

= 0.8271   .....ans