Question

he 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? (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? (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? (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 points. The probability of the Iowa Energy scoring more points than the Maine Red Claws %.

Answer 1

SOLUTION

Solution Develcp a spcad sheet model The spicodsheet mode that simulates the points scoye d by cach and the diffevence in thei Doint totals The procedue in Analytic solver plat form Eo simulhte the Points 騁, click the Analytic Solvev Platfovm tab in the Ribbon. 2 Select the torget cel 3) click Povameters the pmetes group -select simulation > scoyed byh teamsuvittan boloe Ente the values fnto values -or loccv u) click ok dick options in the Cptions gvoup > Entev the vequived simulatior value in the box nextEo 6 Simulations to Run G. click Ok 1. Select the taget cell for vesults g. click Results ' the s' mulation modet ayop-)selert statistic ond click ean -Select the ronge accorcling ly o mean the spyead sheet ode in Anyc lve Pat fowm that Simulat es the points stoved by ac team is as shon belos

NBA-DL lowa Esery Maiee Red Claws Lower Bosad Uppor Boan Lower Boand Upper Bound PsilurUnisorm C6.DS 7347 15 10 PsilntUnisoC10.DIO 6 -hilathisem(C11,D11) 12 7 13 8 lowa Eser SUMB6 813)+PsiOuput Maise Red Claws 15 Total Polsts 17 Standard Deviatloa Polats 18 9 Poist Differestial 20 Meas Peist Differential 21 Standard Deviation Point Differestial-PsiSdDev(B19 B15-F15+Psiopu 24 Plowa Energy Wi)
a

b

The results obtained from the Analytic Solver Platform for cell B15 are as shown below: 8515 4 5004 12 1234 47.051 8515 Mean 84 5004 SuDev: 12 12645476 h Pec 5 5th Perc 104 Standard Deviation 003 357975 86 74 200 Number of Ousters Ouster toshow Advanced Stabistics Mean Abs Deviation 9.4179632 001 100 34504 5819 The mean or average value s the ist monent of the 120 60 100 The lowa Energy score an average of approximately 84.5 points with a standard deviation of 12.1 points. The distribution of points is bell-shaped that is approximately the central limit theorem. normal as a result of

The results obtained from the Analytic Solver Platform for cell F15 are as shown below: PS1 Statstics 73 8.000 8.7753974 7007 023594 F$15 Mear 8 0001 Perc t Parc 103 004 400 85 61 003 S6 002 3293 001 100 Hean he nean or average value is the ist monent of the 70 80 90 110 The Maine Red Claws score an average of approximately 88.0 points with a standard deviation of 8.8 points. The distribution of points is bell-shaped that is approximately normal as a result of the central limit theorem
c
The results obtained from the Analytic Solver Platform for cell B19 are as shown below: งเ S.0 223634 8S1O 0 02 200 Clustern 001 400 200 200 The average point differential is -3.5 points with a standard deviation of 15.0 points. The distribution of point differential is bell-shaped that is approximately normal. These observations provide empirical proof that the difference of two independent normal random variables is normally distributed with a mean equal to the difference in the means of the two underlying random variables (-3.5 84.5-88) and a variance equal to the sum of the variances of the two underlying random variables (224147 77)

2 Tthe losa enevgy has approximately a040 piy o Scoving move points than the Maine Red clacs. OXna
e

The results obtained from the Analytic Solver Platform for cell B15 are as shown below: 8515 119 4 500 21.1127 660% BS15 Mean 4 5001 SDew 211127349 Standad Deviation 007805 34874 4 5Perc 119 002 150 156 142 8 Clustering 100 001 3 Advanced Statistics 223 558 49519 001 50 150 50 The average lowa Energy point total remains the same that is 84.5 points, but the standard deviation of the Energy point total increases to 21.1 points. The results obtained from the Analytic Solver Platform for cell B23 are as shown below

B523 requenay Cumulaive Frequency Reverse Cumulative Frequency Senstivity Scater Plots Staistics 0.4372 Standand Deviaion 0.48606526 Mean 04372 StdDev: 0496065286 0.26081 0253357 1.906 Pere 0 95m Perc:1 0.40 4000 umber of Clusters 020 B Advanced Statistiks Mean Abs. Deiation04211232 The mean or average value is the ist monent of the dstrbution of trials 06 02 04 The probability of the lowa Energy scoring more points than the Maine Red Claws increases to 0.44