Answer
The middle 95% lies between 19 and 23 days.
Work Step by Step
$\mu$ =21, $\sigma$ = 1
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 = 1 , \mu= 21, z = 1.96, z = -1.96 $ into z = $\frac{x - \mu}{\sigma}$ and solve for x:
z = $\frac{x - \mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = $21 + (-1.96 \times 1)$
$x$ = $19.04$ days
$x$ $\approx$ 19 days
z = $\frac{x - \mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = $21 + (1.96 \times 1)$
$x$ = $22.96$ days
$x$ $\approx$ 23 days
The middle 95% lies between 19 and 23 days.
