Answer
$P(19 < x < 21)$ = 0.4772
Work Step by Step
$\mu$ = 21, $\sigma$ = 1
Want to find $P(19 < x < 21)$:
i) Convert 19 to a z-score:
z = $\frac{x - \mu}{\sigma}$
z = $\frac{19 - 21}{1}$
z= -2
ii) Convert 21 to a z score:
z = $\frac{21 - 21}{1}$
z = 0
iii) $P(19 < x < 21) = P(-2 < z < 0)$
$P(-2 < z < 0) = P(z < 0) - P(z < -2) = 0.5 - 0.0228 = 0.4772$
Therefore $P(19 < x < 21)$ = 0.4772
