Chapter 2.1, Problem 36E

To determine

To find: which bowler gets the higher score in his own league

Answer to Problem 36E

Bill, because his standardized score is higher than George’s.

Explanation of Solution

Given:

For 1^st bowler

  $x=180,\mu =150,\sigma =20$

For 2^nd bowler

  $x=190,\mu =160,\sigma =15$

Formula used:

  $Z=\frac{x-\mu }{\sigma }$

Calculation:

Formula for z=score

  $\begin{array}{c}Z=\frac{x-\mu }{\sigma }\\ Z_{George}=\frac{180-150}{20}=1.5\\ Z_{Bill}=\frac{190-160}{15}=2\end{array}$

  $Z_{Bill}>Z_{George}$

So the correct choice is (b)