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surprised? (d) How many points should you expect the player to score if all of these are 3-point shots? (e) If this player randomly takes half of the shots from 3-point range and half from 2-point range and makes both with 25% chance, how many points should you expect the player to score? (Type an imeyer vi a utcimal.)

surprised? (d) How many points should you expect the player to score if all of these are 3-point shots? (e) If this player randomly takes half of the shots from 3-point range and half from 2-point range and makes both with 25% chance, how many points should you expect the player to score? (Type an imeyer vi a utcimal.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Understanding Binomial Probability in Basketball** **Introduction:** In this exercise, we explore the application of a binomial model to predict basketball shooting performance. A hypothetical scenario is provided where a basketball player takes 20 field shots during a game with a 25% success rate. **Exercise Details:** 1. **Assumptions for a Binomial Model:** - The player attempts 20 shots, each shot is independent with a 25% probability of success. - Assumptions: - Each shot is an independent event. - The probability of making a shot remains constant at 25% for each attempt. - These assumptions are reasonable under controlled conditions but may vary in a real game scenario due to factors like player fatigue or defensive pressure. 2. **Expected Number of Baskets:** - You can calculate the expected number of successful shots by multiplying the total attempts by the probability: - \( E(x) = n \times p = 20 \times 0.25 = 5 \) baskets. 3. **Surprise Factor for Success Over 11 Shots:** - Given the low success probability, hitting more than 11 shots is unlikely. - Assessment: - The result is surprising: The probability of this occurring is 0.001. - Answer choice: - **B. Yes, you should be surprised because the probability of this occurring is 0.001.** 4. **Expected Points Scored with 3-Point Shots:** - If all successful shots are 3-pointers: - Expected points = \( 3 \times \text{Expected baskets} = 3 \times 5 = 15 \) points. 5. **Mixed Range Shots Calculation:** - If half of the shots are taken from 3-point range and half from 2-point range: - Both shot types have a 25% success rate. - Calculate expected points: - \( \text{3-point shots: } 10 \times 0.25 \times 3 = 7.5 \) - \( \text{2-point shots: } 10 \times 0.25 \times 2 = 5 \) - Total expected points = \( 7.5 + 5 = 12.5 \) points. **Conclusion:** This exercise illustrates the use of binomial probability to estimate
Transcribed Image Text:**Title: Understanding Binomial Probability in Basketball** **Introduction:** In this exercise, we explore the application of a binomial model to predict basketball shooting performance. A hypothetical scenario is provided where a basketball player takes 20 field shots during a game with a 25% success rate. **Exercise Details:** 1. **Assumptions for a Binomial Model:** - The player attempts 20 shots, each shot is independent with a 25% probability of success. - Assumptions: - Each shot is an independent event. - The probability of making a shot remains constant at 25% for each attempt. - These assumptions are reasonable under controlled conditions but may vary in a real game scenario due to factors like player fatigue or defensive pressure. 2. **Expected Number of Baskets:** - You can calculate the expected number of successful shots by multiplying the total attempts by the probability: - \( E(x) = n \times p = 20 \times 0.25 = 5 \) baskets. 3. **Surprise Factor for Success Over 11 Shots:** - Given the low success probability, hitting more than 11 shots is unlikely. - Assessment: - The result is surprising: The probability of this occurring is 0.001. - Answer choice: - **B. Yes, you should be surprised because the probability of this occurring is 0.001.** 4. **Expected Points Scored with 3-Point Shots:** - If all successful shots are 3-pointers: - Expected points = \( 3 \times \text{Expected baskets} = 3 \times 5 = 15 \) points. 5. **Mixed Range Shots Calculation:** - If half of the shots are taken from 3-point range and half from 2-point range: - Both shot types have a 25% success rate. - Calculate expected points: - \( \text{3-point shots: } 10 \times 0.25 \times 3 = 7.5 \) - \( \text{2-point shots: } 10 \times 0.25 \times 2 = 5 \) - Total expected points = \( 7.5 + 5 = 12.5 \) points. **Conclusion:** This exercise illustrates the use of binomial probability to estimate
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