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?

Answer 1

$6,000

Step-by-step explanation:

The standard deviation of the sampling distribution of the mean is a measure of the difference between the observed values and the mean in a dataset. It is calculated using the formula:

σм= σ/
`√(n) \\`

σ= standard deviation

n= sample size

σм= $12,000/
`√(4)`

σм= $12,000/2

σм= $6,000

The standard deviation for the sampling distribution of the sample mean is $6,000.

Answer 2

The standard deviation for the sampling distribution of the sample mean is 6000.

Step-by-step explanation:

Standard deviation of the population is given as 12000 and we know that the sample has 4 electricians and therefore the standard error is 12000/sqrt(4) = 6000

Therefore , The standard deviation for the sampling distribution of the sample mean is 6000.