for a new type of tire a NASCAR team found the average dista

for a new type of tire, a NASCAR team found the average distance a set of tires would run during a race is 128 miles, with a standard deviation on 14 miles. Assume that tire mileage is independent and follows a Normal model. What is the probability they won\'t have to change tires a third time (and use a fourth set of tires) before the end of a 500-mile race?

Solution

Average distance = X is normal (128, 14)

the probability they won\'t have to change tires a third time (and use a fourth set of tires) before the end of a 500-mile race

= Prob that average life exceeds 125

P(X>125)

=P(Z>-3/14)

=0.5+0.0832

= 0.5832