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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
ANswer the correct answer please.
![**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**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2F4f59276f-8c4b-4ae1-9beb-feb4d9918ef0%2Fzopfz4b_processed.png&w=3840&q=75)
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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