Question

# The annual salary for one particular occupation is normally​ distributed, with a mean of about ​\$127,000...

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.

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

Mean of the sampling distribution = = 127000

Standard deviation of the sampling distribution = = 2757.764

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