Question

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

Convert to z-scores:
z1 = (65−67)/2.5 = −0.8, z2 = (72−67)/2.5 = 2.0.

P(65 ≤ X ≤ 72) = Φ(2.0) − Φ(−0.8) = 0.97725 − 0.21186 ≈ 0.76539 = 76.5%.

So about 76.5% of the students.