Question

Baseball salaries Brad Lidge played a crucial role as the Phillies’ “closer,” pitching the end of many games throughout the season. Lidge’s salary for the $2008$ season was $\$6,350,000$

(a) Find the percentile corresponding to Lidge’s salary. Explain what this value means.

(b) Find the z-score corresponding to Lidge’s salary. Explain what this value means.

Short answer

Part (a) The pay of $75.86$ percent of the players on the $2008$ World Champion Philadelphia Phillies baseball team is less than L's.

Part (b) L's salary was $0.79$ standard deviations above the mean salary of $\$3,388,617$

Step-by-step solution

Part (a) Step 1. Given

For the $2008$ season, Lidge was paid $\$6,350,000$

Let's use the dot plot and salary summary statistics for players on the $2008$ World Champion Philadelphia Phillies baseball team to figure out the following.

Part (a) Step 2. Concept 

The formula used: $z=\frac{x-\mu }{\sigma }$

Part (a) Step 3. Calculation

calculated at the percentile below.

$$\begin{gathered} percentile=22/29 \\ =0.7586 \\ =75.86\% \end{gathered}$$

This means that on the World Champion $2008$ Philadelphia Phillies baseball team, $75.86\%$ of the players' salaries were less than L's. Therefore, $75.86\%$ player's salary on the World Champion $2008$ Philadelphia Phillies baseball team is less than L's salary.

Part (b) Step 1. Calculation

The standardized salary score for L may be found below.

$$\begin{gathered} z=x-\mu /\sigma \\ =\frac{6,350,000-3,388,617}{3,767,484} \\ =0.79 \end{gathered}$$

L's pay was $0.79$ standard deviations higher than the national average of $\$3,388,617$

Therefore, L's salary was $0.79$ standard deviations above the mean salary of $\$3,388,617$