Assume that womens heights are normally distributed with a m

Assume that women\'s heights are normally distributed with a mean given by u=64.5 in, and a standard deviation given by o=2.2 in.

a. If 1 woman is randomly selected, find the probability that her height is less than 65 in.

b. If 41 women are randomly selected, find the probability that they have a mean height less than 65 in.

Solution

Assume that women\'s heights are normally distributed with a mean given by u=64.5 in, and a standard deviation given by o=2.2 in.

a. If 1 woman is randomly selected, find the probability that her height is less than 65 in.

z value of 65, z = (65-64.5)/2.2 = 0.23

P( x < 65) = P( z < 0.23) = 0.591

b. If 41 women are randomly selected, find the probability that they have a mean height less than 65 in.

standard error = sd /sqrt(n) =2.2/sqrt(41) =0.3436

z value of 65, z = (65-64.5)/0.3436 = 1.46

P( mean x < 65) = P( z < 1.46) = 0.9279