Question

given a normally distributed data set with the mean = 80 and the standard deviation = 8, according to the empirical rule, what percent of the data points are below 64? type your answer without using the percent symbol.

Explanation:

Step1: Calculate the number of standard deviations from the mean

The value is \(64\), the mean \(\mu = 80\), and the standard deviation \(\sigma=8\).
We find \(z=\frac{64 - 80}{8}=\frac{- 16}{8}=-2\)

Step2: Sum up the percentages

From the empirical rule (the normal distribution curve percentages), the percentage of data below \(\mu - 2\sigma\) is \(2.35\%+0.15\% = 2.5\%\)

Answer:

\(2.5\)