Question

The tread life of tires mounted on light duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is more than 66,000 miles?

Answer 1

Answer: 0.0013

Explanation:

Given : The test scores are normally distributed with

Mean :
`\mu=\ 60,000`

Standard deviation :
`\sigma= 4,000`

Sample size :
`n=4`

The formula to calculate the z-score :-

`z=(x-\mu)/((\sigma)/(√(n)))`

For x = 66,000

`z=(66000-60000)/((4000)/(√(4)))=3`

The p-value =
`P(z>3)\=1-P(z<3)=1- 0.9986501\approx0.0013`

Hence, the likelihood the mean tire life of these four tires is more than 66,000 miles = 0.0013