Answer
The probability that a randomly selected sixth-grade student reads between 110 and 130 words per minute is 0.3189
Work Step by Step
$\mu$ = 125, $\sigma$ = 24
Want to find $P(110 < x < 130)$:
i) Convert 110 to a z-score:
z = $\frac{x - \mu}{\sigma}$
z = $\frac{110 - 125}{24}$
z $\approx$ -0.63
ii) Convert 130 to a z score:
z = $\frac{130 - 125}{24}$
z $\approx$ 0.21
iii) $P(110 < x < 130) = P(-0.63 < z < 0.21)$
$P(-0.63 < z < 0.21)$
$= P(z \leq 0.21) - P(z \leq -0.63) = 0.5832 - 0.2643 = 0.3189$
Therefore $P(110 < x < 130) = 0.3189$
