Step 1 :Suppose the lengths of human pregnancies are normally distributed with \(\mu=266\) days and \(\sigma=16\) days. The area to the left of \(X=245\) under the normal curve is 0.0947.
Step 2 :This area represents the proportion of human pregnancies that last less than 245 days. This is because the area under the curve of a probability distribution represents the probability of an event occurring. In this case, the event is a human pregnancy lasting less than 245 days.
Step 3 :The area is given as 0.0947, which means that approximately 9.47% of human pregnancies last less than 245 days.
Step 4 :The second interpretation of the area is the probability that a randomly selected human pregnancy lasts less than 245 days. This is because in a probability distribution, the probability of an event is the area under the curve for that event.
Step 5 :In this case, the event is a human pregnancy lasting less than 245 days, and the probability is given by the area to the left of \(X=245\), which is 0.0947 or 9.47%.
Step 6 :Final Answer: \(\boxed{1.\ The\ proportion\ of\ human\ pregnancies\ that\ last\ less\ than\ 245\ days\ is\ 0.0947\ or\ 9.47\%.}\)
Step 7 :Final Answer: \(\boxed{2.\ The\ probability\ that\ a\ randomly\ selected\ human\ pregnancy\ lasts\ less\ than\ 245\ days\ is\ 0.0947\ or\ 9.47\%.}\)