Use the 68-95-99.7 rule to solve the problem.
-The annual precipitation for one city is normally distributed with a mean of 27.5 inches and a standard deviation of 3.2 inches. Fill in the blanks. In $99.7 \%$ of the years, the precipitation in this city is between __ and inches.
A) $21.1,27.5$
B) $27.5,37.1$
C) $21.1,33.9$
D) $17.9,37.1$

Question

Quizplus · Accepted Answer

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean. Therefore, to find the range of precipitation in 99.7% of the years, we calculate the mean minus three times the standard deviation and the mean plus three times the standard deviation: $27.5 - 3(3.2)$ and $27.5 + 3(3.2)$, which gives us $17.9$ and $37.1$ inches, respectively.

Use the 68-95-99 99.7%99.7 \%99.7% Of the Years, the Precipitation in This City Is Between

Use the 68-95-99 $99.7 \%$ Of the Years, the Precipitation in This City Is Between