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.

Answer 1

The probability that the person is between 65 and 69 inches is 0.5403

Explanation:

Mean height =
`\mu = 66`

Standard deviation =
`\sigma = 2.5`

We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)

`Z=(x-\mu)/(\sigma)`

At x = 65

`Z=(65-66)/(2.5)`

Z=-0.4

Refer the z table for p value

P(x<65)=0.3446

At x = 69

`Z=(69-66)/(2.5)`

Z=1.2

P(x<69)=0.8849

So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403

Hence the probability that the person is between 65 and 69 inches is 0.5403