A researcher interested in the age at which women are having their first child surveyed a simple random sample of 250 women having at least one child and found an approximately normal distribution with a mean age of 27.3 and a standard deviation of 5.4. According to the empirical rule, also known as the 68-95-99.7 rule, approximately 95% of the women had their first child between the ages of:

A. 11 years and 43.5 years
B. 16.5 years and 38.1 years
C. 18.7 years and 37.9 years
D. 23.5 years and 33.1 years

According to the empirical rule, also known as the 68-95-99.7 rule, approximately 95% of the data falls within two standard deviations of the mean in a normal distribution. In this case, the mean age at which women are having their first child is 27.3 years, and the standard deviation is 5.4 years. Therefore, to find the age range in which approximately 95% of the women had their first child, we need to calculate two standard deviations above and below the mean.

Two standard deviations below the mean: 27.3 - (2 * 5.4) = 16.5 years

Two standard deviations above the mean: 27.3 + (2 * 5.4) = 38.1 years

Therefore, approximately 95% of the women had their first child between the ages of 16.5 years and 38.1 years.

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