In an all boys school, the heights of the student body are normally distributed with a mean of 67 inches and a standard deviation of 2.5 inches. What percentage of the students are between 65 and 72 inches tall, to the nearest tenth?

Answer 1

First, we need to determine the z-scores for the heights of 65 inches and 72 inches:

For 65 inches:
z = (65 - 67) / 2.5 = -0.8

For 72 inches:
z = (72 - 67) / 2.5 = 2.0

Next, we use a standard normal distribution table or a calculator to find the percentages associated with these z-scores:

- The percentage of students below 65 inches is approximately 21.43%
- The percentage of students below 72 inches is approximately 97.72%

Therefore, the percentage of students between 65 and 72 inches tall is approximately 97.72% - 21.43% = 76.29%. Rounding to the nearest tenth, we get 76.3%.

So, approximately 76.3% of the students at the all boys school are between 65 and 72 inches tall.