Question

I am having a hard time with these types of questions. Could someone show me how to break it down so I know how to do them.

The distribution of sample means for monthly employee income at a particular company for samples of 70 employees is​ normal, with a mean of $5522, and a standard deviation of $224. You take a random sample of 70 employees from the company and find that their mean monthly income is $5,800. How many standard deviations is the sample mean from the mean of the sampling​ distribution? Round to the nearest tenth as needed.

Answer 1

$\mu$ = 5522

$\sigma$ = 224

n = 70

SE = $\sigma$/$\sqrt{n}$

= 224/$\sqrt{70}$

= 26.7731

So,

Z = (5800 - 5522)/26.7731 = 10.38

So,

Answer is:

10.38