Question

The annual salary for one particular occupation is normally distributed, with a mean of about $127,000 and a standard deviation of about $17,000. Random samples of 38 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution.

Answer #1

Solution:

Given that ,

= 127,000

= 17,000

A sample of size n = 38 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 127000

SD = = 17000/38 = 2757.764

**Answer :**

**Mean of the sampling distribution =
= 127000**

**Standard deviation of the sampling distribution =
= 2757.764**

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