Question

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

Answer 1

Step-by-step explanation:

Since the life expectancy of a particular brand of tire is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where,

x = life expectancy of the brand of tire in miles.

µ = mean

σ = standard deviation

From the information given,

µ = 40000 miles

σ = 5000 miles

The probability that a randomly selected tire will have a life of exactly 47,500 miles

P(x = 47500)

For, x = 47500

z = (40000 - 47500)/5000

  = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.067