Chapter 5, Problem 1E

Stats test The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was –2. How many points did he score?

To determine

Find the number of points scored by Gregor.

Answer to Problem 1E

The number of points scored by Gregor is 65.

Explanation of Solution

Given info:

In a Stats exam, the mean score is 75 points and the standard deviation of score is 5 points. The z-score of Gregor is –2.

Justification:

The z-score of a variable X taking value x is,

$z=\frac{x-\mu }{\sigma }$.

Where $\mu$ is the mean and $\sigma$ is the standard deviation of the variable X.

From the above equation, the number of points scored by Gregor can be obtained as follows:

$x=z\sigma +\mu$

Substitute $z=-2$, $\sigma =5$ and $\mu =75$

$\begin{array}{c}x=\left(-2\right)\left(5\right)+75\\ =65\end{array}$

Thus, the number of points scored by Gregor is 65.