Problem 16-09

The Iowa Energy are scheduled to play against the Maine RedClaws in an upcoming game in the National Basketball AssociationDevelopmental League (NBA-DL). Because a player in the NBA-DL isstill developing their skills, the number of points he scores in agame can vary. Assume that each player's point production can berepresented as an integer uniform variable with the ranges providedin 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 byeach team. What is the average and standard deviation of pointsscored by the Iowa Energy? If required, round your answer to onedecimal place.
   
   Average =
   
   Standard Deviation =
   
   What is the shape of the distribution of points scored by the IowaEnergy?
   
   
   
2. What is the average and standard deviation of points scored bythe Maine Red Claws? If required, round your answer to one decimalplace.
   
   Average =
   
   Standard Deviation =
   
   What is the shape of the distribution of points scored by the MaineRed Claws?
   
   
   
3. Let Point Differential = Iowa Energy points - Maine Red Clawpoints. What is the average point differential between the IowaEnergy and Maine Red Claws? If required, round your answer to onedecimal place.
   
   
   
   What is the standard deviation in the point differential?
   
   
   
   What is the shape of the point differential distribution?
   
   
   
4. What is the probability of that the Iowa Energy scores morepoints than the Maine Red Claws? If required, round your answer tothree decimal places.
   
   
   
5. The coach of the Iowa Energy feels that they are the underdogand is considering a \"riskier\" game strategy. The effect of theriskier game strategy is that the range of each Energy player'spoint 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]. Howdoes the new strategy affect the average and standard deviation ofthe Energy point total?
   
   Average =
   
   Standard Deviation =
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewedand considered by your instructor.
   
   
   
   How is the probability of the Iowa Energy scoring more points thatthe Maine Red Claws affected? If required, round your answer tothree decimal places.
   
   Probability =
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewedand considered by your instructor.