Chapter 5.6, Problem 7E

Let X equal the maximal oxygen intake of a human on a treadmill where the measurements are in milliliters of oxygen per minute per kilogram of weight. Assume that, for a particular population, the mean of X is $\mu =54.030$ and the standard deviation is $\sigma =5.8$.

Let $\bar{X}$ be the sample mean of a random sample of size $n=47$.

Find $P\left(52.761\le \bar{X}\le 54.453\right)$, approximately.