Normal Probability Distribution

Instructions

Use the table and the data provided to analyze the 2015/2016 points per game for the LA Lakers.

Players

Average points per game 2015/2016

x

Deviation from the Mean

(x)

Square of the Deviation

(x)

z-Score

x

Anthony Brown

4.0

-0.787

0.6194

-0.109

Brandon Bass

7.2

2.413

5.8226

0.334

D'Angelo Russell

13.2

8.413

70.779

1.163

Jordan Clarkson

15.5

10.713

114.77

1.481

Julius Randle

11.3

6.513

42.419

0.900

Kobe Bryant

17.6

12.813

164.17

1.771

Larry Nance Jr.

5.5

0.713

0.508

0.099

Louis Williams

15.3

10.513

110.52

1.453

Marcelo Huertas

4.5

-0.287

0.082

-0.04

Metta World Peace

5.0

0.213

0.045

0.029

Nick Young

7.3

2.513

6.315

0.347

Robert Sacre

3.5

-1.287

1.656

-0.178

Roy Hibbert

5.9

1.113

1.238

0.154

Ryan Kelly

4.2

-0.587

0.0345

-0.081

Tarik Black

3.4

-1.387

1.924

-0.192

Total

x = 4.787

(x ) = 52.358

Standar Deviation: 7.236

Work: Second Column/ 7.236

Sum of z-scores: 7.131

Source: http://www.espn.com/nba/team/stats/_/name/lal/los-angeles-lakers

Part A: Complete the table. (5 points)

1. Calculate the mean () for the players listed.
2. Fill in the table by calculating the deviation from the mean, (x ), the square of the deviation, (x ), and the sum of the squares of the deviation.
3. Calculate the variance.
4. Calculate the standard deviation.
5. Calculate the z-score for each player.

Part B: Answer the following questions. (15 points)

1. What does the z-score determine?
2. Analyze the player's average points per game that is farthest from the mean. Evaluate the z-score and justify whether it is reasonable.
3. Analyze the player's average points per game that is closest to the mean. Evaluate the z-score and justify whether it is reasonable.
4. Explain why negative z-scores are present.
5. What is the sum of the z-scores? Evaluate your calculation and justify it with statistical reasoning.

Part C: Compare the data. (10 points)

Use the table presented below for z-scores for the salaries of the LA Lakers in 2015/2016.

Player

Salary 2015/2016

x

z-Score

x

Anthony Brown

$525,093

0.65

Brandon Bass

$3,000,000

0.27

D'Angelo Russell

$5,103,120

0.05

Jordan Clarkson

$845,059

0.60

Julius Randle

$3,132,240

0.25

Kobe Bryant

$25,000,000

3.07

Larry Nance Jr.

$1,155,600

0.55

Lou Williams

$7,000,000

0.33

Marcelo Huertas

$525,093

0.65

Metta World Peace

$1,499,187

0.50

Nick Young

$5,219,169

0.06

Robert Sacre

$981,358

0.58

Roy Hibbert

$15,514,031

1.63

Ryan Kelly

$1,724,250

0.47

Tarik Black

$845,059

0.60

Source: http://www.lakersnation.com/los-angeles-lakers-salaries/

Choose two players from the table above. Use the average points per game data and salary data of the players you chose to determine which of your two players is paid more. Is this fair? Use your z-score data to help in your explanation. Be sure to justify your reasoning.