Assume that full term birth weights are normally distributed

Assume that full term birth weights are normally distributed with mean 3350 grams and standard deviation 440 grams.

Let X be the birth weight for a randomly chosen full term baby.

a) We want to find the probablity that the weight of a randomly chosen full term baby exceeds 3200 grams. Write the event in terms of X and find the probablity.

Solution

X follows Normal distibution with mean=3350 and standard deviation=440

So the probability is

P(X>3200) = P((X-mean)/s >(3200-3350)/440)

=P(Z>-0.34) =0.6331 (from standard normal table)