Question

Tyrell and Bruno are two baseball pitchers from different leagues. Tyrell has 25 strikeouts this year in a league with a mean of 20 strike outs and a standard deviation of 3.6.Bruno has 23 strike outs this year in a league with a mean of 19 strike outs and astandard deviation of 2.4. Which pitcher is relatively better? (Hint: Z-score!)

Answer 1

Given data:

For Tyrell

`\begin{gathered} x=25 \\ \bar{x}=20 \\ \sigma=3.6 \\ \end{gathered}`

For Bruno

`\begin{gathered} x=23 \\ \bar{x}=19 \\ \sigma=2.4 \end{gathered}`

Method: Find the z-score for the two of them

Find the z-score for Tyrell

`z=\frac{x-\bar{x}}{\sigma}=(25-20)/(3.6)=1.389`

Find the z-score for Bruno

`z=\frac{x-\bar{x}}{\sigma}=(23-19)/(2.4)=1.667`

To determine the pitch that is relatively better, we will find the probabilities of the two using the z-score tables and determine which is closest to one

For Tyrell, a z-score of 1.389 corresponds to 0.4176

For Bruno, a z-score of 1.667 corresponds to 0.4522

Therefore, since Bruno has a higher z-score and a higher probability, then his pitcher is relatively better