Question

The number of driving miles before a certain type of tire begins to show wear is on the average 18,200 miles with a standard deviation σ = 3,500 miles. If Jack Car Rental Agency buys 25 of these tires for replacement purposes and parts each one on a different car, compute the mean μ x̅ and standard deviation σ x̅ of the sampling distribution of the sample means.

Answer 1

We'll use the properties of sampling distributions of sample means.

The mean:

$\mu_{\bar x} =\mu=18200$ miles.

Standard deviation:

$\sigma_{\bar x}=\cfrac{\sigma}{\sqrt n}=\cfrac{3500}{\sqrt {25}}=700$ miles.