Question

The mean height of women in a country​ (ages 20-​29) is 64.1 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 ​inches? Assume σ=2.58.

The probability that the mean height for the sample is greater than 65 inches is ______ .

(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

mean = = 64.1

standard deviation = = 2.58

n = 70

= 64.1 and

= / n = 2.58 / 70

P(​ > 65) = 1 - P( < 108) = 1- P(( - ) / < (64.1 - 65) / 2.58/70) = 1 - P(z < -2.92)

    Using standard normal table,

P( > 65) = 1 - 0.0018 = 0.9982

Probability = 0.9982