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 5 inches. What percentage of the students are between 59 and 80 inches tall, to the nearest tenth?

Answer 1

z1 = (59−67)/5 = −1.6, z2 = (80−67)/5 = 2.6.
P(59≤X≤80) = Φ(2.6) − Φ(−1.6) ≈ 0.9953 − 0.0548 = 0.9405 ≈ 94.1%.