Question

The annual salary for one particular occupation is normally​ distributed, with a mean of about ​$133 comma 000 and a standard deviation of about ​$15 comma 000. Random samples of 28 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. The mean is mu Subscript x over bar equals nothing​, and the standard deviation is sigma Subscript x over bar equals nothing.The annual salary for one particular occupation is normally​ distributed, with a mean of about ​$133 comma 000 and a standard deviation of about ​$15 comma 000. Random samples of 28 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. The mean is mu Subscript x over bar equals nothing​, and the standard deviation is sigma Subscript x over bar equals nothing.

Answer 1

Solution :

Given that,

$\mu$_{$\bar x$} = 133000

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 15000 / $\sqrt$ 28 = 2834.73354

124495.801 127350.534 150165267 153000 135331.733 13869 466