Question

The average height of a woman aged 20-29 is 64 inches with a standard deviation of 2.75 inches. What is the probability of selecting 25 women with average height more than 65 inches?

Answer 1

The probability of selecting 25 women with average height more than 65 inches is 0.036

Explanation:

To calculate the probability of selecting 25 women with average height more than 65 inches, we need to calculate the z-statistic of the sample with average height 65 inches.

z-score can be calculated as follows:

z(65) =
`(X-M)/((s)/(√(N) ) )` where

• X = 65 inches
• M is the average height of women aged 20-29 (64 inches)
• s is the standard deviation (2.75 inches)
• N is the sample size (25)

Then z(65) =
`(65-64)/((2.75)/(√(25) ) )` ≈ 1.818

The probability of a statistic being bigger then this statistic is 0.036