Question

suppose the lengths of human pregnancies are normally distributed with μ = 266 days and σ = 16 days. complete parts (a) and (b) below.
(a) the figure to the right represents the normal curve with μ = 266 days and σ = 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 245 days is 0.0947
b. the probability that a randomly selected human pregnancy lasts more than days is
(b) the figure to the right represents the normal curve with μ = 266 days and σ = 16 days. the area between x = 280 and x = 295 is 0.1558. provide two interpretations of this area.

Explanation:

For part (a), when dealing with a normal distribution, the area under the curve to the left of a value \(x\) can be interpreted in two ways. One is in terms of proportion: the proportion of the population (in this case, human pregnancies) that have a value (length of pregnancy) less than \(x\). The other is in terms of probability: the probability that a randomly - selected individual from the population (a randomly - selected human pregnancy) has a value (length of pregnancy) less than \(x\).

For part (b), similar interpretations apply. The area between two values \(x_1\) and \(x_2\) in a normal distribution can be interpreted as the proportion of the population (human pregnancies) whose values (lengths of pregnancy) lie between \(x_1\) and \(x_2\). It can also be interpreted as the probability that a randomly - selected individual from the population (a randomly - selected human pregnancy) has a value (length of pregnancy) between \(x_1\) and \(x_2\).

Answer:

• For part (a):
• First interpretation: The proportion of human pregnancies that last less than \(245\) days is \(0.0947\).
• Second interpretation: The probability that a randomly selected human pregnancy lasts less than \(245\) days is \(0.0947\).
• For part (b):
• First interpretation: The proportion of human pregnancies that last between \(280\) and \(295\) days is \(0.1558\).
• Second interpretation: The probability that a randomly selected human pregnancy lasts between \(280\) and \(295\) days is \(0.1558\).