Answer to Question #331400 in Statistics and Probability for zimp

Question

1. An average tire used by a transportation company lasts 20,000 km with a standard deviation of 100 km. Assuming that the distance traveled by a tire is normally distributed, what is the probability that a tire used by the company will last at most 30,000 km?

Answer 1

We have a normal distribution, $\mu=20000, \sigma=100.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{30000-20000}{100}=100;\\ P(X\le148)=P(Z\le100)=1.0000\\ \text{ (from z-table) } .$