Chapter 12, Problem AP4.34CPT

To determine

To find out what will the mean and the standard deviation of the new scores be.

Answer to Problem AP4.34CPT

Option (b) is the correct option.

Explanation of Solution

It is given in the question that:

  $\begin{array}{l}{\mu }_X=60\\ {\sigma }_X=18\end{array}$

Thus, as we know the properties of mean and the standard deviation as:

  $\begin{array}{l}{\mu }_{aX+b}=a{\mu }_X+b\\ {\sigma }_{aX+b}=a{\sigma }_X\end{array}$

Then we will obtain for $2X-5$ , by:

  $\begin{array}{l}{\mu }_{2X-5}=2{\mu }_X-5\\ =2(60)-5\\ =115\\ {\sigma }_{2X-5}=a{\sigma }_X\\ =2(18)\\ =36\end{array}$

Thus, the option (b) is the correct option.