Answer
The middle 95% falls between 77.96 and 172.04 words.
Work Step by Step
$\mu$ =125, $\sigma$ = 24
i ) z- score corresponding to lower 2.5% percentile (area of 0.025) = -1.96
ii) z-score corresponding to upper 2.5% = 1.96
iii) Sub $\sigma = 24 , \mu= 125, z = 1.96, z = -1.96 $ into z = $\frac{x - \mu}{\sigma}$ and solve for x:
z = $\frac{x - \mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = $125 + (-1.96 \times 24)$
$x$ = $77.96$ words
z = $\frac{x - \mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = $125 + (1.96 \times 24)$
$x$ = $172.04$ words
