Question

suppose the lengths of human pregnancies are normally distributed with $mu = 266$ days and $sigma = 16$ days. complete parts (a) and (b) below
(a) 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 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

Explanation:

In a normal distribution, the area under the curve represents proportions or probabilities. When we talk about the area to the left of a value \(X\), in the context of human pregnancies (where \(X\) represents the length of pregnancy in days), one interpretation is in terms of proportion. The proportion of a population (here, human pregnancies) that has a characteristic (length less than a certain number of days) is given by the area. Another interpretation is in terms of probability. The probability of randomly selecting an individual from the population (a human pregnancy) with a characteristic (length less than a certain number of days) is also given by the area under the normal - curve for the relevant region.

Answer:

For the first part:
A. The proportion of human pregnancies that last less than \(245\) days is \(0.0947\)

For the second part:
A. The probability that a randomly selected human pregnancy lasts less than \(245\) days is \(0.0947\)