Question

The tread life on tires produced at one factory has a standard deviation of sigma equals 4 comma 000 miles. What is the standard deviation of the sampling distribution of the sample means given the sample size is 4

Answer 1

`\sigma_x = 2000`

Explanation:

Given

`\sigma = 4000`

`n = 4`

Required

The sample standard deviation

The sample standard deviation cannot be calculated directly. However, we can use the value of standard error because standard error approximates to sample standard deviation.

So, we have:

`\sigma_x = (\sigma)/(\sqrt n)`

`\sigma_x = (4000)/(\sqrt 4)`

`\sigma_x = (4000)/(2)`

`\sigma_x = 2000`

Hence, the sample standard deviation is 2000