Question

The top-selling Red and Voss tire is rated 70000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 83000 miles and a standard deviation of 5000 miles.

A. What is the probability that the tire wears out before 70000 miles? Probability =

B. What is the probability that a tire lasts more than 91000 miles? Probability =

Answer 1

Solution :

Given that ,

mean = = 83000

standard deviation = = 5000

A.

P(x < 70000) = P[(x - ) / < (70000 - 83000) /5000 ]

= P(z < -2.6)

= 0.0047

Probability = 0.0047

B.

P(x > 91000) = 1 - P(x < 91000)

= 1 - P[(x - ) / < (91000 - 83000) / 5000]

= 1 - P(z < 1.6)

= 1 - 0.9452

= 0.0548

Probability = 0.0548