Question

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?.

Answer 1

The statement that  describes the sampling distribution of the sample mean is: Approximately normal with mean $206,274 and standard deviation $3,788.

Sampling distribution of the sample mean

Using this formula

Standard deviation= Standard deviation /√Random sample

Where:

Standard deviation=$37,881

Random sample=100

Let plug in the formula

Standard deviation= $37,881/√100

Standard deviation=$37,881/10

Standard deviation=$3,788

Inconclusion the statement that  describes the sampling distribution of the sample mean is: Approximately normal with mean $206,274 and standard deviation $3,788.

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