Chapter 6.2, Problem 54E

To determine

To Calculate: the mean of the total score deduction T for a randomly selected essay.

Answer to Problem 54E

  $\mu =8.3$

Explanation of Solution

Given:

  $\begin{array}{l}{\mu }_X=2.1\\ {\sigma }_X=1.136\\ {\mu }_Y=1.0\\ {\sigma }_Y=1.0\end{array}$

X= number of nonword errors in a randomly selected essay

Y= number of word errors in a randomly selected essay

Calculation:

  $\begin{array}{c}{\mu }_{NW}=3\times {\mu }_X\\ =3\times 2.1\\ =6.3\end{array}$

  $\begin{array}{c}{\mu }_W=2\times {\mu }_Y\\ =2\times 1.0\\ =2.0\end{array}$

  $\begin{array}{c}\mu ={\mu }_{NW}+{\mu }_W\\ =6.3+2.0\\ =8.3\end{array}$

If every data for non word error multiply by 3, then the center of the distribution will be multiplied by 3, so the measure of center also required to be multiplied by 3 and the mean is measure of center .Similarly if every data for word error multiply by 2, then the center of the distribution will be multiplied by 2, so the measure of center also required to be multiplied by 2 and the mean is measure of center. The mean of the two random variable will be the sum of their means. The total average 8.3 points are removed for the total number of non word and word errors.