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Let X denote the magnitude of a force applied to a steel beam as a U(400, 500) continuous uniform random variable. There is a 25% chance that the force applied to the beam is less than x. Find x. Answer to the nearest integer. 42 420 485 425 418

Let X denote the magnitude of a force applied to a steel beam as a U(400, 500) continuous uniform random variable. There is a 25% chance that the force applied to the beam is less than x. Find x. Answer to the nearest integer. 42 420 485 425 418

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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**Problem Statement:** Let \( X \) denote the magnitude of a force applied to a steel beam as a \( U(400, 500) \) continuous uniform random variable. There is a 25% chance that the force applied to the beam is less than \( x \). Find \( x \). Answer to the nearest integer. **Options:** - 42 - 420 - 485 - 425 - 418 **Solution Explanation:** In this problem, \( X \) is a continuous uniform random variable defined on the interval \([400, 500]\), which means it has a constant probability density function over this range. The probability \( P(X < x) = 0.25 \). In the setting of a uniform distribution, the probability \( P(X < x) \) can be calculated as follows: \[ P(X < x) = \frac{x - 400}{500 - 400} = 0.25 \] Solving for \( x \): \[ \frac{x - 400}{100} = 0.25 \] \[ x - 400 = 25 \] \[ x = 425 \] Thus, the correct answer is: - **425**
Transcribed Image Text:**Problem Statement:** Let \( X \) denote the magnitude of a force applied to a steel beam as a \( U(400, 500) \) continuous uniform random variable. There is a 25% chance that the force applied to the beam is less than \( x \). Find \( x \). Answer to the nearest integer. **Options:** - 42 - 420 - 485 - 425 - 418 **Solution Explanation:** In this problem, \( X \) is a continuous uniform random variable defined on the interval \([400, 500]\), which means it has a constant probability density function over this range. The probability \( P(X < x) = 0.25 \). In the setting of a uniform distribution, the probability \( P(X < x) \) can be calculated as follows: \[ P(X < x) = \frac{x - 400}{500 - 400} = 0.25 \] Solving for \( x \): \[ \frac{x - 400}{100} = 0.25 \] \[ x - 400 = 25 \] \[ x = 425 \] Thus, the correct answer is: - **425**
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