Question

The mean height of women in a country​ (ages 20−​29) is 63.9 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 ​inches? Assume σ=2.75.

The probability that the mean height for the sample is greater than 64 inches is

Answer 1

Given that ,

mean = = 63.9

standard deviation = = 2.75

n = 75

= 63.9

= / n = 2.75/ 75 = 0.317542648

P( >64 ) = 1 - P( <64 )

= 1 - P[( - ) / < (64 -63.9) /0.317542648 ]

= 1 - P(z < 0.32)

Using z table

= 1 - 0.6255

= 0.3745

probability=0.3745