EXAMPLE 6.4 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 100 departures estimates the mean departure delay of all the departures in the population. The population standard deviation for the more than 210,000 departures in the population of Figure 6.1(a) is minutes. From Example 6.3, we know minutes. By the 95 part of the 68–95–99.7 rule, about 95% of all samples will have its mean within two standard deviations of , that is, within ±5.16 of .