Chapter 2.1, Problem 12E

To determine

To compute: the standardized batting average for C, W, and B.

Answer to Problem 12E

All three hitters were at least 4 standard deviations above their peers, but W’s Z -score is the highest.

Explanation of Solution

Given:

  

Calculation:

Cobb's batting average was 0.420 in 1911. The standardized score for Cobb is obtained below.

  $\begin{array}{l}z\left(\text{Cobb}\right)=\frac{x-\mu }{\sigma }\\ =\frac{0.420-0.266}{0.0371}\\ \approx 4.15\end{array}$

William's batting average was 0.406 in 1941. The standardized score for William is obtained below.

  $\begin{array}{l}z\left(\text{William}\right)=\frac{x-\mu }{\sigma }\\ =\frac{0.406-0.267}{0.0326}\\ \approx 4.26\end{array}$

Brett's batting average was 0.390 in 1980. The standardized score for Brett is obtained below.

  $\begin{array}{l}z\left(\text{Brett}\right)=\frac{x-\mu }{\sigma }\\ =\frac{0.390-0.261}{0.0317}\\ \approx 4.07\end{array}$

All three hitters were at least 4 standard deviations above their peers, but Williams

Z -score is the highest.

Conclusion:

Therefore, all three hitters were at least 4 standard deviations above their peers, but W’s Z -score is the highest.