**Title: Probability Calculations with Continuous Uniform Distribution****Problem Description:**The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable \(X\) having a continuous uniform distribution with \(A = 9\) and \(B = 12\). **Calculate the following probabilities:**1. The probability that on a given day the amount of coffee dispensed by this machine will be: - (a) at most 11.4 liters; - (b) more than 9.4 liters but less than 11.2 liters; - (c) at least 10.8 liters.**Detailed Questions and Answers:**Based on the given continuous uniform distribution properties, we need to solve for the following probabilities with appropriate simplification of the answers:**(a) The probability is [___].***(Simplify your answer.)***(b) The probability is [___].***(Simplify your answer.)***(c) The probability is [___].***(Simplify your answer.)***Solution Explanation:**For a continuous uniform distribution \(X \sim \text{Uniform}(A, B)\), the probability density function \(f(x)\) is defined as:\[ f(x) = \frac{1}{B - A}, \text{ for } A \le x \le B \]Given \(A = 9\) and \(B = 12\):\[ f(x) = \frac{1}{12 - 9} = \frac{1}{3} \]**(a) Probability that \(X\) is at most 11.4 liters:**\[ P(X \leq 11.4) = \int_{9}^{11.4} f(x) \, dx = \int_{9}^{11.4} \frac{1}{3} \, dx = \frac{11.4 - 9}{3} = \frac{2.4}{3} = 0.8 \]So, **(a) The probability is \(0.8\).****(b) Probability that \(X\) is more than 9.4 liters but less than 11.2 liters:**\[ P(9.4 < X < 11.2) = \int_{9.4}^{11.2} \

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Answered: The daily amount of coffee, in liters,…

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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