Question

18
type the correct answer in the box. use numerals instead of words.
the mean of a normally distributed dataset is 12, and the standard deviation is 2.
% of the data points lie between 8 and 16.

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the data - point.
For $x = 8$, $z_1=\frac{8 - 12}{2}=\frac{-4}{2}=-2$.
For $x = 16$, $z_2=\frac{16 - 12}{2}=\frac{4}{2}=2$.

Step2: Use the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within $z=- 2$ and $z = 2$.

Answer:

95