Question

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random. Find the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100

Answer 1

Answer:  5

Step-by-step explanation:

We know that the standard deviation of the sampling distribution of the means is given by :_

$SE=\sigma_x=\dfrac{\sigma}{\sqrt{n}}$

Given : The average weekly earnings for employees in general automotive repair shops is$\mu=\ 450$.

The standard deviation for the weekly earnings for such employees =$\sigma= \ 50.$

Now, the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size$n=100$:-

$SE=\sigma_x=\dfrac{50}{\sqrt{100}}\\\\\Rightarrow\ SE=\dfrac{50}{10}\\\\\Rightarrow\ SE=5$

Hence, the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100 = 5