The Iowa Wolves 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. Develop a spreadsheet model that simulates the points scoredby each team. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the following table. (Use at least 1,000 trials.)Player12345678Iowa Wolves Maine Red Claws[5,20][7, 20][5, 10][10, 40][7, 20][2, 10][2,5][2, 4]What is the standard deviation?What is the shape of the distribution?O uniformObell-shapedO skewed leftO skewed rightskewed leftO skewed rightWhat is the standard deviation?7.95[6, 12](a) Consider the points scored by the Iowa Wolves team. (Round your answers to two decimal places.)What is the average of points scored?What is the shape of the distribution?Ⓒ uniformO bell-shaped[15, 20][10, 20][15, 30][6, 10][1,20][1,4](b) Consider the points scored by the Maine Red Claws. (Round your answers to two decimal places.)What is the average of points scored?83X[2, 4](c) Let Point Differential = Iowa Wolves points - Maine Red Claw points. (Round your answers to two decimal places.)What is the average point differential between the Iowa Wolves and Maine Red Claws?1.64|X What is the standard deviation in the point differential?14.66What is the shape of the point differential distribution?O uniformO bell-shapedskewed leftO skewed right(d) What is the probability that the Iowa Wolves scores more points than the Maine Red Claws? (Round your answer to three decimal places.)(e) The coach of the Iowa Wolves feels that they are the underdog and is considering a riskier game strategy. The effect of this strategy that the range of each Wolves player's point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Wolves player 1's range with therisky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Wolves point total? (Round your answers to two decimal places.)averagepointspointsstandard deviationWhat is the new probability of the Iowa Wolves scoring more points than the Maine Red Claws? (Round your answer to three decimal places.)

Points of the players are represented as:PlayerIowa WolvesMaine Red Claws1[5, 20][6, 12]2[7, 20][15, 20]3[5, 10][10, 20]4[10, 40][15, 30]5[7, 20][6, 10]6[2, 10][1, 20]7[2, 5][1, 4]8[2, 4][2, 4]Use the following Python code to simulate the model.#Import the random generator moduleimport random # Define the player rangesiowa_wolves_ranges = [[5, 20], [7, 20], [5, 10], [10, 40], [7, 20], [2, 10], [2, 5], [2, 4]]maine_red_claws_ranges = [[6, 12], [15, 20], [10, 20], [15, 30], [6, 10], [1, 20], [1, 4], [2, 4]]# Number of trialsnum_trials = 1000# Initialize lists to store resultsiowa_wolves_total_points = []maine_red_claws_total_points = []point_differentials = []# Simulate the game for each trialfor _ in range(num_trials): iowa_points = sum(random.randint(min_range, max_range) for min_range, max_range in iowa_wolves_ranges) maine_points = sum(random.randint(min_range, max_range) for min_range, max_range in maine_red_claws_ranges) # Calculate point differential point_differential = iowa_points - maine_points # Store results iowa_wolves_total_points.append(iowa_points) maine_red_claws_total_points.append(maine_points) point_differentials.append(point_differential)# Print results print(f"Iowa Wolves' Total Points for {num_trials} Trials:")print(iowa_wolves_total_points)print(f"Maine Red Claws' Total Points for {num_trials} Trials:")print(maine_red_claws_total_points)print(f"Point Differentials for {num_trials} Trials:")print(point_differentials)Save this code as points.py on desktop.Open command prompt and write:cd>desktopPython points.pyThis code will generate 1000 team totals for each team and also 1000 differentials.Let's use snippets from the code above and write the new code that will included average and standard deviation of the two teams over 1000 simulations. Differential point average and standard deviation will also be computed.#Import modules to generate random numbers and to perform statistical calculations.import randomimport statistics# Define the player rangesiowa_wolves_ranges = [[5, 20], [7, 20], [5, 10], [10, 40], [7, 20], [2, 10], [2, 5], [2, 4]]maine_red_claws_ranges = [[6, 12], [15, 20], [10, 20], [15, 30], [6, 10], [1, 20], [1, 4], [2, 4]]# Number of trialsnum_trials = 1000# Initialize lists to store results from each run of the simulationiowa_wolves_total_points = []maine_red_claws_total_points = []point_differentials = []# Simulate the game for each trialfor _ in range(num_trials): iowa_points = sum(random.randint(min_range, max_range) for min_range, max_range in iowa_wolves_ranges) maine_points = sum(random.randint(min_range, max_range) for min_range, max_range in maine_red_claws_ranges) # Calculate point differential point_differential = iowa_points - maine_points # Store results iowa_wolves_total_points.append(iowa_points) maine_red_claws_total_points.append(maine_points) point_differentials.append(point_differential)# Subpart (b): Calculate the average and standard deviation of points scored by the Iowa Wolvesaverage_iowa_wolves_points = statistics.mean(iowa_wolves_total_points)std_deviation_iowa_wolves_points = statistics.stdev(iowa_wolves_total_points)print(f"Average Points Scored by Iowa Wolves: {average_iowa_wolves_points:.2f}")print(f"Standard Deviation of Points Scored by Iowa Wolves: {std_deviation_iowa_wolves_points:.2f}")# Subpart (c): Calculate the average and standard deviation of points scored by the Maine Red Clawsaverage_maine_red_claws_points = statistics.mean(maine_red_claws_total_points)std_deviation_maine_red_claws_points = statistics.stdev(maine_red_claws_total_points)print(f"Average Points Scored by Maine Red Claws: {average_maine_red_claws_points:.2f}")print(f"Standard Deviation of Points Scored by Maine Red Claws: {std_deviation_maine_red_claws_points:.2f}")Step 4: Calculate differential of points scored by the two teams# Subpart (d): Calculate the average and standard deviation of the point differentialaverage_point_differential = statistics.mean(point_differentials)std_deviation_point_differential = statistics.stdev(point_differentials)print(f"Average Point Differential: {average_point_differential:.2f}")print(f"Standard Deviation of Point Differential: {std_deviation_point_differential:.2f}")# Subpart (e): Calculate the probability that the Iowa Wolves score more points than the Maine Red Clawswinning_count = sum(1 for diff in point_differentials if diff > 0)probability_winning = winning_count / num_trialsprint(f"Probability that Iowa Wolves score more points than Maine Red Claws: {probability_winning:.3f}")Run this code to get an output around the shown values below.With this strategy, the ranges of points of players in Iowa wolves team change.New range is as follows:iowa_wolves_ranges = [[0, 25], [0, 27], [0, 15], [0, 50], [0, 27], [0, 12], [0, 7], [0, 6]]With this new range, we can perform the calculations again to find new average, standard deviation and probability of winning.Code:import randomimport statistics# Define the player rangesiowa_wolves_ranges = [[0, 25], [0, 27], [0, 15], [0, 50], [0, 27], [0, 12], [0, 7], [0, 6]]maine_red_claws_ranges = [[6, 12], [15, 20], [10, 20], [15, 30], [6, 10], [1, 20], [1, 4], [2, 4]]# Number of trialsnum_trials = 1000# Initialize lists to store resultsiowa_wolves_total_points = []maine_red_claws_total_points = []point_differentials = []# Simulate the game for each trialfor _ in range(num_trials): iowa_points = sum(random.randint(min_range, max_range) for min_range, max_range in iowa_wolves_ranges) maine_points = sum(random.randint(min_range, max_range) for min_range, max_range in maine_red_claws_ranges) # Calculate point differential point_differential = iowa_points - maine_points # Store results iowa_wolves_total_points.append(iowa_points) maine_red_claws_total_points.append(maine_points) point_differentials.append(point_differential)# Subpart (b): Calculate the average and standard deviation of points scored by the Iowa Wolvesaverage_iowa_wolves_points = statistics.mean(iowa_wolves_total_points)std_deviation_iowa_wolves_points = statistics.stdev(iowa_wolves_total_points)print(f"Average Points Scored by Iowa Wolves: {average_iowa_wolves_points:.2f}")print(f"Standard Deviation of Points Scored by Iowa Wolves: {std_deviation_iowa_wolves_points:.2f}")# Subpart (c): Calculate the average and standard deviation of points scored by the Maine Red Clawsaverage_maine_red_claws_points = statistics.mean(maine_red_claws_total_points)std_deviation_maine_red_claws_points = statistics.stdev(maine_red_claws_total_points)print(f"Average Points Scored by Maine Red Claws: {average_maine_red_claws_points:.2f}")print(f"Standard Deviation of Points Scored by Maine Red Claws: {std_deviation_maine_red_claws_points:.2f}")# Subpart (d): Calculate the average and standard deviation of the point differentialaverage_point_differential = statistics.mean(point_differentials)std_deviation_point_differential = statistics.stdev(point_differentials)print(f"Average Point Differential: {average_point_differential:.2f}")print(f"Standard Deviation of Point Differential: {std_deviation_point_differential:.2f}")# Subpart (e): Calculate the probability that the Iowa Wolves score more points than the Maine Red Clawswinning_count = sum(1 for diff in point_differentials if diff > 0)probability_winning = winning_count / num_trialsprint(f"Probability that Iowa Wolves score more points than Maine Red Claws: {probability_winning:.3f}")Output:Parts a-e output:Part f output The probability that Iowa wolves score more is higher with the new strategy. The average points scored is slightly lower but the standard deviation is significantly higher than the previous strategy.

The lowa Wolves 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. Develop a spreadsheet model that simulates the points scored by each team. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the following table. (Use at least 1.000 trials.) Player lowa Wolves Maine Red Claws [5. 201 [6.12] [7.20] (5. 10) [10,40] [7.20] [2. 10) [2.5] 1 2 3 4 5 6 7 What is the standard deviation? (a) Consider the points scored by the lowa Wolves team. (Round your answers to two decimal places.) What is the average of points scored? What is the shape of the distribution? O uniform bell-shaped O skewed left O skewed right What is the standard deviation? 7.05✔ [15, 20) [10, 20) [15.30] (b) Consider the points scored by the Maine Red Claws. (Round your answers to two decimal places.) What is the average of points scored? What is the shape of the distribution? uniform [6.10] [1,20] O bell-shaped O skewed left O skewed right (e) Let Point Differential Iowa Wolves points Maine Red Claw points. (Round your answers to two decimal places.) What is the average point differential between the lowa Wolves and Maine Red Claws? 1.04 1x

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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