Normal Distribution Question:

Question

The heights of adult males are normally distributed with the following parameters

Mean: 70 inches

Standard Deviation: 3 inches

Task 1: The average NBA player is 6'7", or 79 inches tall. What is the probability that if you select an adult male at random, they will be as tall as or taller than the average NBA player? (that is, greater than 79 inches tall)

Task 2: What is the probability that a random adult male is under 6', or 72 inches tall?

Task 3: What is the probability that a random adult male is between 67 and 74 inches tall?

Answer 1

mean 70

standard deviation = 3

3 standard deviations above the mean = 70+3(3) = 79

by the empirical rule 99.7% are less than 3 SD's from the mean

0.3% are above 79 inches tall.

pick a male at random, probability is 0.3% that he's > 79 inches tall.

to do the remaining parts of the problem, you'll need z tables or a z calculator to calculate the area under the normal curve

Under 72 inches is z=(72-70)/3 = 2/3. z=2/3=about 0.6667

area to the left of z is .7475. Probability of less than 72 inches is about 74.75%

P(67<x<74) is the area under the normal curve from z=-1 to z=4/3. It's over 68% using the empirical rule. Use z tables or a z calculator for a closer approximation.

.68/2+.4088 = 0.7488 = 74.88%

or even closer approximation:

.3413 +.4088 = .7501 = 75.01%