Assume that womens heights are normally distributed with a m

Assume that women\'s heights are normally distributed with a mean given by u=62.1 in, and a standard deviation o=2.6 in.

a) if 1 women is randomly selected, find the probability that her height is between 61.5 inches and 62.5 inches

b) if 16 women are randomly slected, find the probabiliy that they have a mean height between 61.5 in and 62.5 in

Solution

Let, X = the weight of any randomly selceted woman

a) P [ 61.5 < X < 62.5 ] = P [ ( 61.5 - 62.1) / 2.6 < Z < ( 62.5 - 62.1) / 2.6 ]
   = P [ Z < 0.1538462 ] - P [ Z < -0.2307692 ] = 0.5611345 - 0.408747 = 0.1523875...

b) P [  61.5 < X < 62.5 ] = P [ ( 61.5 - 62.1) / ( 2.6/ sqrt(16) ) < Z < ( 62.5 - 62.1) / ( 2.6 / sqrt(16) ) ]
=  P [ Z < 0.6153846 ] - P [ Z < -0.9230769 ] = 0.7308496 - 0.1779836 = 0.5528661..