The weights of 1824 year old women are normally distributed

The weights of 18-24 year old women are normally distributed with a mean of 132 pounds and a standard deviation of 27.4. If one randomly selected 150 of these women ages 18-24, how many of them would be expected to weight 100-150 pounds.

Solution

P(100<X<150) = P((100-132)/27.4 <(X-mean)/s <(X-mean)/s <(150-132)/27.4 )

=P(-1.17<Z<0.66)

=0.6244 (from standard normal table)

So 150*0.6244 =93.66