Chapter 3.1, Problem 3.5E

(a)

To determine

To calculate the value of percentile for Lidge’s salary.

Answer to Problem 3.5E

77.58^th percentile

Explanation of Solution

Given:

Player	Salary	Player	Salary	Player	Salary
Burrell, Pat	1,42,50,000	Romero, J. C.	32,50,000	Kendrick, Kyle	4,45,000
Howard, Ryan	1,00,00,000	Feliz, Pedro	30,00,000	Dobbs, Greg	4,40,000
Myers, Brett	85,83,333	Helms, Wes	24,00,000	Ruiz, Carlos	4,25,000
Rollins, Jimmy	80,00,000	Werth, Jayson	17,00,000	Condrey, Clayton	4,20,000
Eaton, Adam	79,58,333	Madson, Ryan	14,00,000	Coste, Chris	4,15,000
Utley, Chase	77,85,714	Durbin, Chad	9,00,000	Rosario, Francisco	3,95,000
Lidge, Brad	63,50,000	Taguchi, So	9,00,000	Zagurski, Mike	3,92,500
Moyer, Jamie	60,00,000	Bruntlett, Eric	6,00,000	Lahey, Tim	3,90,000
Gordon, Tom	55,00,000	Hamels, Cole	5,00,000	Mathieson, Scott	3,90,000
Jenkins, Geoff	50,00,000	Victorino, Shane	4,80,000

  

Variable	Salary
n	29
Mean	3388617
Standard deviation	3767484
Minimum	390000
Quartile 1	440000
Median	1400000
Quartile 3	6000000
Maximum	14250000

Formula used:

  $\text{Percentile = }\left(\frac{\text{No}\text{. of values less than }x+0.5}{\text{Total no}\text{. of values }}\right)\times 100$

Calculation:

  $\begin{array}{c}\text{Percentile = }\left(\frac{\text{No}\text{. of values less than }x+0.5}{\text{Total no}\text{. of values }}\right)\times 100\\ =\left(\frac{22+0.5}{29}\right)\times 100\\ ={77.58}^{\text{Th }}\text{percentile}\end{array}$

The 77.58^th percentile means that 77.58% of all player have salary less than Lidge’s salary.

(b)

To determine

To calculate the value of z score for Lidge’s salary.

Answer to Problem 3.5E

Z =0.786

Explanation of Solution

Calculation:

  $\begin{array}{l}z=\frac{6350000-3388617}{3767484}\\ z=0.786\end{array}$

The z score equal to 0.786 means that Lidge’s salary is 0.786 standard deviation above than mean.