Chapter 2.1, Problem 36E

To determine

To select: the best answer for the given question.

Answer to Problem 36E

The correct option is “b”

Explanation of Solution

Given:

1. Bill, because his 190 is higher than George’s 180.
2. Bill, because his standardized score is higher than George’s.
3. Bill and George have the same rank in their leagues, because both are 30 pins above the mean.
4. George, because his standardize score is higher than Bill’s.
5. George, because the standard deviation of bowling scores is higher in his league.

Calculation:

The summary statistics are:

	Score, x	µ	s
George	180	150	20
Bill	190	160	15

Find the z-scores for George and Bill respectively.

  $\begin{array}{l}{z}_{George}=\frac{x-\mu }{\sigma }\\ =\frac{180-150}{20}\\ =1.5\\ z_{Bill}=\frac{x-\mu }{\sigma }\\ =\frac{190-160}{15}\\ =2\end{array}$

Bill’s score is 2 standard deviations above the mean while George’s score is 1.5 standard deviations above the mean.

So the correct option is

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

Conclusion:

Therefore, the correct option is “b”