Assume that womens heights are normally distributed with a m

Assume that women\'s heights are normally distributed with a mean given by =63.2 in and a standard deviation given by =2.7 in. If 1 woman is randomly selected, find the probability that her height is less than 64 in.If 44 women are randomly selected, find the probability that they have a mean height less than 64 in.

Solution

Normal Distribution
Mean ( u ) =63.2
Standard Deviation ( sd )=2.7
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 64) = (64-63.2)/2.7/ Sqrt ( 1 )
= 0.8/2.7= 0.2963
= P ( Z <0.2963) From Standard NOrmal Table
= 0.6165                  
                  
b)
P(X < 64) = (64-63.2)/2.7/ Sqrt ( 44 )
= 0.8/0.407= 1.9654
= P ( Z <1.9654) From Standard NOrmal Table
= 0.9753