### Understanding Probability in Basketball Free Throws#### ScenarioWhen practicing basketball, Rachel has a 67% chance of making a free throw. She shoots 12 free throws. Let the random variable \( X \) be the number of free throws she makes.#### Problem 1: Probability Calculation**Question:** Find the probability she makes exactly 5 free throws. Give your answer to at least three nonzero decimal places.**Input Box:** ```plaintext[ ]```#### Problem 2: Expected Value Calculation**Question:** What is the expected value of \( X \)? Interpret this value.**Input Box:** ```plaintext[ ]```### ExplanationIn this problem, we are dealing with a binomial distribution scenario where the probability of each free throw is constant (67%) and each trial (free throw) is independent of the others. We will calculate the probability for Rachel making exactly 5 free throws out of 12 attempts, and then compute the expected number of successful free throws.

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When practicing basketball, Rachel has a 67% chance of making a free throw. She shoots 12 free throws. Let the random variable X be the number of free throws she makes. Find the probability she makes exactly 5 free throws. Give your answer to at least three nonzero decimal places. What is the expected value of X. Interpret this value.

When practicing basketball, Rachel has a 67% chance of making a free throw. She shoots 12 free throws. Let the random variable X be the number of free throws she makes. Find the probability she makes exactly 5 free throws. Give your answer to at least three nonzero decimal places. What is the expected value of X. Interpret this value.

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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