Question

numeric 2 points
given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what percent of the data points
above 76?
numeric 2 points
given a normally distributed data set with the mean = 28 and the standard deviation = 4, according to the empirical rule, what percent of the data points
below 24?
answer
16
type your answer without using the percent symbol.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\). Here, \(x = 76\), \(\mu=88\), and \(\sigma = 6\).

$$z=\frac{76 - 88}{6}=\frac{- 12}{6}=-2$$

Step2: Use the Empirical Rule

The Empirical Rule states that for a normal distribution:

• Approximately \(95\%\) of the data lies within \(\mu\pm2\sigma\) (i.e., \(z=-2\) to \(z = 2\)).
• The percentage of data less than \(z=-2\) is \(\frac{100 - 95}{2}=2.5\%\)

Answer:

\(2.5\)