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Sampling Distributions and Nurse's Salaries

APSTAT-EYNLEY

A typical nurse's salary (in dollars) can range from $\$25,000$ to $\$55,000$ per year. A computer is programmed to randomly choose $20$ nurse's salaries from among the $200$ nurses employed at a hospital and compute the standard deviation.

The computer repeats this process a total of $50$ times. The sampling distribution of the standard deviation of the nurse's salaries is shown below.

One of the points on this sampling distribution, $\$8,165$, is highlighted.

What does this value represent?

A

Six nurses have a salary lower than $\$8,165$.

B

$\$8,165$ is an unusually low value for a nurse's salary at this hospital.

C

There is a $14\%$ chance that the population standard deviation is $\$8,165$.

D

The standard deviation for one randomly selected sample of nurse's salaries was $\$8,165$.

E

The average standard deviation for the samples of nurse's salaries is $\$8,165$.