The length of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting 280 days or longer

Question

The length of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15  days.  Find the probability of a pregnancy lasting 280 days or longer

kirbykirby · Answer

Let $X$ be the number of days a pregnancy lasts. The question asks you for P$(X\ge 280)$. WHat you must do is standardize $X$ and then you'll be able to use a standard normal table:

$$P(X\ge 280)=P\left( \frac{X-268}{15}\ge\frac{280-268}{15}\right)=P(Z\ge0.8) $$