Question

7. The lifetime of a certain brand of tires is approximately normally distributed, with a

mean of 40,000 miles and a standard deviation of 2,500 miles under normal driving conditions.

Tire wear is greatly affected by road, weather and driver conditions along with proper

maintenance of the tires. A driver who aggressively accelerates or makes quick stops, for

example, will wear out a tire much more quickly. The brand carries a warranty of 33,000 miles

under normal driving conditions, i.e., the company will replace a tire if it wears out before this

mileage limit is reached.

Answer 1

0.0025551

Explanation:

Given that:

Mean (m) = 40000

Standard deviation (s) = 2500

P(x < 33,000) :

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (33000 - 40000) / 2500 = - 2.8

p(Z < -2.8) = 0.0025551 ( Z probability calculator)

Probability of Tyre wagering out before mileage limit is reached = 0.0025551