Problem

Suppose the lengths of human pregnancies are normally distributed with $\mu=266$ days and $\sigma=16$ days. Complete parts (a) and (b) below. The figure to the right represents the normal curve with $\mu=266$ days and $\sigma=16$ days. The area to the left of $X=245$ is 0.0947 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

Solution

Step 1 :Suppose the lengths of human pregnancies are normally distributed with \(\mu=266\) days and \(\sigma=16\) days.

Step 2 :The figure to the right represents the normal curve with \(\mu=266\) days and \(\sigma=16\) days. The area to the left of \(X=245\) is 0.0947.

Step 3 :The area under the curve of a probability distribution represents the probability of an event occurring. In this case, the area to the left of \(X=245\) represents the probability that a randomly selected human pregnancy lasts less than 245 days.

Step 4 :This is because the area to the left of a point on a normal distribution curve represents the probability of a value being less than that point.

Step 5 :Therefore, the correct choice is A. The probability that a randomly selected human pregnancy lasts less than 245 days is 0.0947 or 9.47%.

Step 6 :Final Answer: \(\boxed{A. The probability that a randomly selected human pregnancy lasts less than 245 days is 0.0947 or 9.47\%}\).

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Source: https://solvelyapp.com/problems/20015/

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