Question

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians’ yearly earnings is normally distributed and that the standard deviation is σ = $12,000.

Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?

• 6,000

• 12,000

• 36,000

• 54,000

Answer 1

On average, an electrician earn approximately $54,000 per year in the United States.

Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is $12,000.

A sample of 4 electricians is taken.

We have to find the standard deviation of the sampling distribution of this sampling mean.

We know, that the formula of standard deviation of sampling distribution is given by

$s=\frac{\sigma}{\sqrt{n}}$

Where, sigma is the population standard deviation; and n is the sample size.

Here,

$\sigma=12000$

$n=4$

Here,

12000 12000 S 6000 n 2

The correct answer is

Standard deviation for the sampling distribution of the sample mean is option (A) 6,000.