Let X be the length of a pregnancy in days X is a continuous

Let X be the length of a pregnancy in days. X is a continuous random variable with a normal distribution. Its mean is 266 days and its standard deviation is 16 days. What is the variance of X?________________ What is the probability that a randomly selected pregnancy lasts more than 274 days?

Solution

So the variance of X is 16^2 =256

So the probability that a randomly selected pregnancy lasts more than 274 days is

P(X>274) = P((X-mean)/s >(274-266)/16)

=P(Z>0.5) = 0.3085 (from standard normal table)