Suppose the lengths of human pregnancies are normally distributed with $\mu=266$ days and $\sigma=16$ days. Complete parts (a) and (b) below. normal curve with $\mu=266$ days and $\sigma=16$ days. The area to the left of $X=245$ is 0.0947 . Provide two interpretations of this area.
Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.)
A. The proportion of human pregnancies that last less than 245 days is 0.0947 .
B. The proportion of human pregnancies that last more than days is
Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.)
A. The probability that a randomly selected human pregnancy lasts less than days is
B. The probability that a randomly selected human pregnancy lasts more than days is
Answer
Final Answer: \(\boxed{2.\ The\ probability\ that\ a\ randomly\ selected\ human\ pregnancy\ lasts\ less\ than\ 245\ days\ is\ 0.0947\ or\ 9.47\%.}\)
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: \(\boxed{2.\ The\ probability\ that\ a\ randomly\ selected\ human\ pregnancy\ lasts\ less\ than\ 245\ days\ is\ 0.0947\ or\ 9.47\%.}\)
