Question

9) Statistical information for a data set is given. • The mean is 18.1. • The Z-score for 13.0 is -1.7. What is the standard deviation for this data set? A 1.7 B 3.0 C 3.4 D 5.1

Answer 1

The Solution.

Step 1:

We shall state the formula for Z-statistics.

$\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ \text{Where Z=z-score}=-1.7 \\ \mu=\operatorname{mean}=18.1 \\ \sigma=s\tan dard\text{ deviation=?} \\ x=\text{sample}=13.0 \end{gathered}$

Step 2:

We shall substitute the above values into the formula.

$\begin{gathered} -1.7=\frac{13.0-18.1}{\sigma} \\ \text{Cross multi\lbrack{}plying, we get} \\ -1.7\sigma=-5.1 \\ \text{Dividing both sides by -1.7, we get} \\ \sigma=\frac{-5.1}{-1.7}=3.0 \end{gathered}$

Step 3:

Presentation of the Answer.

Thus, the correct answer is 3.0 (option B)