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,