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 between $x=235$ and $x=300$ is 0.9569 . 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. Use ascending order.) A. The proportion of human pregnancies that last between and days is B. The proportion of human pregnancies that last less than $\square$ or more than days is
Solution
Step 1 ：The area under the curve of a probability distribution represents the probability of an event occurring. In this case, the area between \(x=235\) and \(x=300\) represents the probability of a pregnancy lasting between 235 and 300 days. This can be interpreted in two ways:
Step 2 ：The proportion of human pregnancies that last between 235 and 300 days is 0.9569.
Step 3 ：The proportion of human pregnancies that last less than 235 days or more than 300 days is 1 - 0.9569 = 0.0431.
Step 4 ：Final Answer: The proportion of human pregnancies that last less than 235 days or more than 300 days is \(\boxed{0.0431}\).
