Question

One year Terry had the lowest ERA (eamed-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.45. Also, Alice had the lowest ERA of any female pitcher at the school with an ERA of 3.03. For the males, the mean ERA was 4.174 and the standard deviation was 0.835 For the females, the mean ERA was 4.605 and the standard deviation was 0.534. Find their respective Z-scores.

Answer 1

Terry's Z-score is -0.867, indicating he performed better than the average male pitcher, while Alice's Z-score of -2.95 shows she performed significantly better compared to the average female pitcher.

Step-by-step explanation:

To calculate Terry and Alice's respective Z-scores, we'll use the formula for a Z-score which is Z = (X - μ) / σ, where X is the value from the dataset, μ (mu) is the mean average, and σ (sigma) is the standard deviation.

For Terry, the male pitcher with an ERA of 3.45:

1. Z-score for Terry = (Terry's ERA - Mean ERA for males) / Standard Deviation for males
2. Z-score for Terry = (3.45 - 4.174) / 0.835
3. Z-score for Terry = -0.724 / 0.835
4. Z-score for Terry = -0.867

For Alice, the female pitcher with an ERA of 3.03:

1. Z-score for Alice = (Alice's ERA - Mean ERA for females) / Standard Deviation for females
2. Z-score for Alice = (3.03 - 4.605) / 0.534
3. Z-score for Alice = -1.575 / 0.534
4. Z-score for Alice = -2.95