Area under Sampling Distribution of the Mean (3 of 4)

---

The formula for z used here is a special case of the general formula for z:



Since the distribution of interest is the distribution of means, the formula can be rewritten as



where M is a sample mean, μ is mean of the distribution of means which is equal to the population mean, and is the standard error of the mean.

In general, when a problem asks about the probability of a mean, the sampling distribution of the mean should be used. The standard error of the mean is used as the standard deviation. Continuing with the calculations,

M = 580
μ= 500
σm= 44.72

and therefore,