Answer
a) $x$ = 73.112 inches
b) $x$ = 67.46 inches
Work Step by Step
PART A
i) Find the z-score that corresponds to 0.90
Using the standard normal distribution table/technology we obtain a value of 1.28
ii) Sub known values into z = $\frac{x - \mu}{\sigma}$ and solve for $x$
1.28 = $\frac{x - 69.4}{2.9}$
$x$ = $69.4$ + $(1.28 \times 2.9)$
$x$ = 73.112 inches
PART B
i) Find the z-score that corresponds to 0.25
Using the standard normal distribution table/technology we obtain a value of -0.67
ii) Sub known values into z = $\frac{x - \mu}{\sigma}$ and solve for $x$
-0.67 = $\frac{x - 69.4}{2.9}$
$x$ = $69.4$ + $(-0.67 \times 2.9)$
$x$ = 67.46 inches
