Question

Problem 12-09

The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association Developmental League (NBA-DL). Because a player in the NBA-DL is still developing his skills, the number of points he scores in a game can vary dramatically. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the table below.

Player	Iowa Energy	Maine Red Claws
1	[5, 20]	[7, 12]
2	[7, 20]	[15, 20]
3	[5, 10]	[10, 20]
4	[10, 40]	[15, 30]
5	[6, 20]	[5, 10]
6	[3, 10]	[1, 20]
7	[2, 5]	[1, 4]
8	[2, 4]	[2, 4]

1. Develop a spreadsheet model that simulates the points scored by each team. What is the average and standard deviation of points scored by the Iowa Energy? If required, round your answer to one decimal place.
   
   Average =
   
   Standard Deviation =
   
   What is the shape of the distribution of points scored by the Iowa Energy?
   
   Bell Shaped
   
2. What is the average and standard deviation of points scored by the Maine Red Claws? If required, round your answer to one decimal place.
   
   Average =
   
   Standard Deviation =
   
   What is the shape of the distribution of points scored by the Maine Red Claws?
   
   Bell Shaped
   
3. Let Point Differential = Iowa Energy points - Maine Red Claw points. What is the average point differential between the Iowa Energy and Maine Red Claws? If required, round your answer to one decimal place. Enter minus sign for negative values.
   
   
   
   What is the standard deviation in the point differential? Round your answer to one decimal place.
   
   
   
   What is the shape of the point differential distribution?
   
   Bell Shaped
   
4. What is the probability of that the Iowa Energy scores more points than the Maine Red Claws? If required, round your answer to three decimal places.
   
   
   
5. The coach of the Iowa Energy feels that they are the underdog and is considering a "riskier" game strategy. The effect of the riskier game strategy is that the range of each Energy player's point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Energy player 1's range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Energy point total? Round your answer to one decimal place.
   
   Average =
   
   Standard Deviation =
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
   How is the probability of the Iowa Energy scoring more points that the Maine Red Claws affected? If required, round your answer to three decimal places.
   
   Probability =

Answer 1

Player	Iowa			Maine
	min	max	Mean	min	max	Mean
1	5	20	12.5	7	12	9.5
2	7	20	13.5	15	20	17.5
3	5	10	7.5	10	20	15
4	10	40	25	15	30	22.5
5	6	20	13	5	10	7.5
6	3	10	6.5	1	20	10.5
7	2	5	3.5	1	4	2.5
8	2	4	3	2	4	3

Player	Iowa	Maine
1	12.5	9.5
2	13.5	17.5
3	7.5	15
4	25	22.5
5	13	7.5
6	6.5	10.5
7	3.5	2.5
8	3	3
Total	84.5	88

(b)

(c)

(d)

The average and standard deviation of Iowa energy is

average: 84.4

standard deviation: 21.1

The standard deviation of the points scored by Iowa energy has increased from 12 to 21.1 . But the average point scored has not changed (83.9 earlier compared to 84.4 now). The new strategy has increased the variation in scored of Iowa energy because the spread (minimum and maximum points scored) of points scored by each player of Iowa energy has increased, but the mean score has remained the same. For example player 1 scores uniformly distributed in [5,20] before the change. The mean is (5+20)/2=12.5. The variance is (25-5)^2/12=33.33. After the change in strategy, player 1 would score in the range [0,25]. The mean score now is (0+25)/2=12.5 (No change). However the variance now is (25-0)^2/12 = 52.08.

The probability of the Iowa Energy scoring more than the Maine is 0.425.