Answer
$P(240 \leq x \leq 280) = 0.76$
Work Step by Step
$\mu =266$, $\sigma = 16$
i) Convert 240 to a z-score:
z = $\frac{x - \mu}{\sigma}$
z = $\frac{240 - 266}{16}$
z= -1.63
ii) Convert 280 to a z-score:
z = $\frac{280 - 266}{16}$
z = 0.88
ii) $P(240 \leq x \leq 280) = P(—1.63 < z < 0.88)$
$P(-1.63 < z < 0.88) = P(x < 0.88) - P(x < -1.63) = 0.8106 - 0.0516 = 0.76$
Therefore, $P(240 \leq x \leq 280) = 0.76$
