in an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and…

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 72$: $z_1=\frac{72 - 71}{3}=\frac{1}{3}\approx0.33$ For $x = 79$: $z_2=\frac{79 - 71}{3}=\frac{8}{3}\approx2.67$

Step2: Use the standard normal table

We want to find $P(0.33<Z<2.67)$. We know that $P(0.33<Z<2.67)=P(Z < 2.67)-P(Z < 0.33)$. From the standard - normal table, $P(Z < 2.67)=0.9962$ and $P(Z < 0.33)=0.6293$.

Step3: Calculate the probability

$P(0.33<Z<2.67)=0.9962 - 0.6293=0.3669$.

Step4: Convert to percentage

To convert the probability to a percentage, we multiply by 100. $0.3669\times100 = 36.7%$ (to the nearest tenth)

Answer:

$36.7%$