Chapter 5.5, Problem 3E

Let X equal the widest diameter (in millimeters) of the fetal head measured between the 16th and 25th weeks of pregnancy. Assume that the distribution of X is $N\left(46.58,40.96\right)$.

Let X be the sample mean of a random sample of $n=16$ observations of X.

(a) Give the values of $E\left(\bar{X}\right)$ and $\mathrm{var}\left(\bar{X}\right)$.

(b) Find $P\left(44.42\le \bar{X}\le 48.98\right)$.