Question

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual. What is the probability that the person is between 65 and 69 inches?

Answer 1

Answer: the probability that the person is between 65 and 69 inches is 0.54

Step-by-step explanation:

Since the height for Asian adult males is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = height for Asian adult males.

µ = mean height

σ = standard deviation

From the information given,

µ = 66 inches

σ = 2.5 inches

We want to find the probability that the person is between 65 and 69 inches. It is expressed as

P(65 ≤ x ≤ 69)

For x = 65

z = (65 - 66)/2.5 = - 0.4

Looking at the normal distribution table, the probability corresponding to the z score is 0.34

For x = 69

z = (69 - 66)/2.5 = 1.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.88

Therefore,

P(65 ≤ x ≤ 69) = 0.88 - 0.34 = 0.54