EXAMPLE 5.7

How close will the sample mean be to the population mean? With the Normal distribution to work with, we can better describe how precisely a random sample of 60 visits estimates the mean length of all visits to the help room. The population standard deviation for the 1264 visits in the population of Figure 5.6(a) is σ = 41.84 minutes. From Example 5.6 we know minutes. By the 95 part of the 68–95–99.7 rule, about 95% of all samples will have mean within two standard deviations of μ, that is, within ±10.8 minutes of μ.