What is the probability that someone on the basketball team is 74 inches or shorter?

Question

The basketball coach likes to recruit tall students. The height of the students are normally distributed. The mean height of the basketball team is 79 inches high with a standard deviation of 1.76 inches. Someone claims to be a member of the team who is 74 inches tall. What is the probability that someone on the basketball team is 74 inches or shorter?

Answer 1

79 - 3 standard deviations = 79 - 3(1.76) = 79 - 5.28 = 73.72

99.7 % of all heights are between 73.72 and 84.28, the remaining .3% is divided in two, with .15% less than 73.2

It's about a 0.15% chance you're 73.2 inches tall. 74 is about the same.

It's about 1/8 of 1% chance you're that "short"

Use z tables or a statistics calculator to get a more precise answer.