Answer
a) $x \approx$ 68.96 inches
b) $x \approx$ 62.26 inches
Work Step by Step
$\mu$ = 64.2, $\sigma$ = 2.9
Part A
1) Find the z score that corresponds to an area of 0.95:
z = 1.64
2) Sub the values in z = $\frac{x - \mu}{\sigma}$ and solve for $x$
z = $\frac{x - 64.2}{2.9}$
$1.64$ = $\frac{x - 64.2}{2.9}$
$x$ = $1.64(2.9) + 64.2$
$x$ $\approx$ 68.96 inches
Part B
1) Find the z score that corresponds to an area of 0.25:
z = -0.67
2) Sub the values in z = $\frac{x - \mu}{\sigma}$ and solve for $x$
z = $\frac{x - 64.2}{2.9}$
$-0.67$ = $\frac{x - 64.2}{2.9}$
$x$ = $-0.67(2.9) + 64.2$
$x$ $\approx$ 62.26 inches