Question

Suppose the heights of the members of a population follow a normaldistribution. If the mean height of the population is 72 inches and thestandard deviation is 3 inches, 95% of the population will have a height within which range?

Answer 1

We get that

$\begin{gathered} P(-a\le Z\le a)=0.95 \\ 1-2\cdot P(Z\le-a)=0.95 \\ P(Z\le-a)=0.025 \\ -a=-1.96\rightarrow a=1.96 \\ 1.96=\frac{X-72}{3} \\ X_2=77.88 \\ X_1=66.12 \end{gathered}$

So the answer is A