Answer
$P(1000 < x < 1400)$ = 0.8658
Work Step by Step
$\mu =1262$
$\sigma = 118$
Part A
i) Convert 1000 to a z-score:
z = $\frac{x - \mu}{\sigma}$
z = $\frac{1000 - 1262}{118}$
z= -2.22
ii) Convert 1400 to a z score:
z = $\frac{1400 - 1262}{118}$
z = 1.17
iii) $P(1000 < x < 1400) = P(—2.22 < z < 1.17)$
$P(-2.22 < z < 1.17)$
= $P(z < 1.17) - P(z < -2.22)$
=$ 0.8790 - 0.0132$
= $0.8658$
Therefore $P(1000 < x < 1400)$ = 0.8658
