A researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child. The survey found an approximately normal distribution with a mean age of 27.3 years and a standard deviation of 5.4 years.

According to the 68-95-99.7 rule, approximately 95% of women had their first child between the ages of:

A. 11.1 years and 43.5 years
B. 16.5 years and 38.1 years
C. 21.9 years and 32.7 years
D. 21.9 years and 38.1 years
E. 25.0 years and 29.6 years

Applying the 68-95-99.7 rule, also known as the empirical rule in statistics, it is concluded that approximately 95% of women had their first child between the ages of 16.5 and 38.1 years.

Explanation:

The question deals with an application of the 68-95-99.7 rule, also known as the empirical rule in statistics. This rule states that for a normal distribution: 68% of data falls within the first standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

The mean age at which women have their first child is given as 27.3 years, with a standard deviation of 5.4 years. To find the range within which roughly 95% of the women had their first child, we need to add and subtract two times the standard deviation to the mean.

So, we get: 27.3 - 2(5.4) = 16.5 years and 27.3 + 2(5.4) = 38.1 years. Therefore, according to the 68-95-99.7 rule, approximately 95% of women had their first child between the ages of 16.5 and 38.1 years, which corresponds to option (B).

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