Question

The mean height of women in a country​ (ages 20−​29) is 64.2 inches. A random sample of 65 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=2.59

Answer 1

Solution :

Given that ,

mean = = 64.2

standard deviation = = 2.59

n = 65

= 64.2

= / n = 2.59 / 65 = 0.32

P( > 65 ) = 1 - P( < 65)

                 = 1 - P(( - ) / < (65 - 64.2) / 0.32)

                 = 1 - P(z < 2.5)

       = 1 - 0.9938    Using standard normal table,

P( >65) = 0.0062

Probability = 0.0062