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?

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