Question

(All answers were generated using 1,000 trials and native Excel functionality.)

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

Player	lowa 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]

Develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals.

(a)	What are the average and standard deviation of points scored by the Iowa Energy?
	Round your answers to one decimal place.
	Average: Standard Deviation:
	What is the shape of the distribution of points scored by the Iowa Energy?
	- Select your answer -Bell-shaped, symmetricUniformBimodalLeft skewedRight skewedItem 3
(b)	What are the average and standard deviation of points scored by the Maine Red Claws?
	Round your answers to one decimal place.
	Average: Standard Deviation:
	What is the shape of the distribution of points scored by the Maine Red Claws?
	- Select your answer -Bell-shaped, symmetricUniformBimodalLeft skewedRight skewedItem 6
(c)	Let Point Differential = Iowa Energy points – Maine Red Claw points. What is the average Point Differential between the Iowa Energy and Maine Red Claws? What is the standard deviation of the Point Differential? If your answer is negative, enter a minus sign in the input box.
	Round your answers to one decimal place.
	Average: Standard Deviation:
	What is the shape of the Point Differential distribution?
	- Select your answer -Bell-shaped, symmetricUniformBimodalLeft skewedRight skewedItem 9
(d)	What is the probability that the Iowa Energy scores more points than the Maine Red Claws?
	Round your answer to the nearest whole number.
	%
(e)	The coach of the Iowa Energy feels that they are the underdog and is considering a riskier game strategy. The effect of this 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? How does that affect the probability of the Iowa Energy scoring more points than the Maine Red Claws?
	Round first two numerical answers to one decimal place and the last answer to a whole percentage.
	The average Iowa Energy point total is relatively unchanged at  points, and the standard deviation of the Energy point total - Select your answer -is relatively unchanged atincreases todecreases toItem 12  points. The probability of the Iowa Energy scoring more points than the Maine Red Claws - Select your answer -is relatively unchanged atincreases todecreases toItem 14  %.

Answer 1

Since we have provided with ranges of points of player of both teams so to have clear picture of performance of players using summary statistics we need to have discrete values from given ranges.

Hence we have taken Mean value of provided range of points.

Refer below screenshot of sheet:

a)

Average of points scored by Lowa Energy = 10.6

Standard deviation of points scored by Lowa Energy =7.2

The shape of Points scored by Lowa Energy is looks like Positively Skewed or Right Skewed distribution.

b)

Average of points scored by Maine Red Claws = 11

Standard deviation of points scored by Maine Red Claws= 6.9

The shape of Points scored by Maine Red Claws team quite looks like Positively Skewed or Right Skewed distribution.

C)

Point Differential is derived by taking Difference between Lowa Energy team player point and Main red Claws team points.

Average of points scored by Point Differential  = -0.4

Standard deviation of points scored by Maine Red Claws= 4.4

This graph of Point differential is not showing any concrete pattern here, still we may say that it quit looks like Negatively skewed or left skewed distribution but not perfectly left skewed.

d)

Since there is no major difference in average points of player of both teams i.e. Lowa Energy = 10.6 and Main Red Claws with 11. Hence we can say there is slightly greater point production in Main Red Claws than Lowa Energy.

Therefore probability that the Iowa Energy scores more points than the Maine Red Claws= 10.6/11= 0.96

e)

New Strategy taken by Lowa energy to increase the point production is not enough effective since Average points obtained by each player production is remains same i.e. Average= 10.6, also there is no major impact on Standard deviation as well i.e. Std Deviation= 7.2