The lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 15 days. a. find the probability of a pregnancy lasting 309 days or longer. b. if the length of pregnancy is in the lowest 4%, then the baby is premature. find the length that separates premature babies from those who are not premature.

Let be the random variable for the length of a pregnancy. follows a normal distribution, so we can transform it to a random variable with the standard normal distribution via the rule



a.




b. A baby is premature if the duration of the pregnancy is up to , where



This percentage corresponds to a value of about -1.75; that is,



To find the corresponding value of , we solve:



meaning a pregnancy has to exceed 242.75 days in duration in order for the baby to not be deemed premature.