The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and 55.55 min. If one such class is randomly selected, find P47 P47- (Report answer accurate to 4 decimal places.) > Next Question
The lengths of a professor's classes has a continuous uniform distribution between 49.29 min and 55.55 min. If one such class is randomly selected, find P47 P47- (Report answer accurate to 4 decimal places.) > Next Question
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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![**Understanding Continuous Uniform Distributions**
This exercise helps us understand continuous uniform distributions through a practical example related to the length of a professor's classes.
**Problem Statement:**
The lengths of a professor's classes follow a continuous uniform distribution between 49.29 minutes and 55.55 minutes. The task is to find the cumulative probability \( P_{47} \), which represents the probability that a randomly selected class lasts 47 minutes or less.
**Given Information:**
- The class duration ranges from 49.29 minutes to 55.55 minutes (minimum = 49.29, maximum = 55.55).
- We need to compute \( P_{47} \), the probability that the class length is 47 minutes or less.
### Solution:
To compute \( P_{47} \), use the formula for the cumulative distribution function (CDF) of a uniform distribution:
\[ P(X \leq x) = \frac{x - a}{b - a} \]
Where:
- \( a \) is the minimum value (49.29 minutes),
- \( b \) is the maximum value (55.55 minutes),
- \( x \) is the value for which we want to find the cumulative probability.
However, since 47 minutes is less than the minimum value of 49.29 minutes in the uniform distribution, \( P_{47} \) will be 0 because the CDF for a uniform distribution at a value less than the minimum is always zero.
\[ P_{47} = 0 \]
### Conclusion:
Therefore, the probability that a randomly selected class lasts for 47 minutes or less is 0.
**Interactive Component:**
Students can input their values and check answers interactively.
**Next Steps:**
* [Next Question](#)
This example illustrates the key concepts of continuous uniform distributions and their computations through an easily understandable problem context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa28b18f-3e2d-4592-9d09-7b963ee49630%2F8b1d273c-b8cb-459e-90d1-d9aa8685b566%2Ftwzo7zr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Continuous Uniform Distributions**
This exercise helps us understand continuous uniform distributions through a practical example related to the length of a professor's classes.
**Problem Statement:**
The lengths of a professor's classes follow a continuous uniform distribution between 49.29 minutes and 55.55 minutes. The task is to find the cumulative probability \( P_{47} \), which represents the probability that a randomly selected class lasts 47 minutes or less.
**Given Information:**
- The class duration ranges from 49.29 minutes to 55.55 minutes (minimum = 49.29, maximum = 55.55).
- We need to compute \( P_{47} \), the probability that the class length is 47 minutes or less.
### Solution:
To compute \( P_{47} \), use the formula for the cumulative distribution function (CDF) of a uniform distribution:
\[ P(X \leq x) = \frac{x - a}{b - a} \]
Where:
- \( a \) is the minimum value (49.29 minutes),
- \( b \) is the maximum value (55.55 minutes),
- \( x \) is the value for which we want to find the cumulative probability.
However, since 47 minutes is less than the minimum value of 49.29 minutes in the uniform distribution, \( P_{47} \) will be 0 because the CDF for a uniform distribution at a value less than the minimum is always zero.
\[ P_{47} = 0 \]
### Conclusion:
Therefore, the probability that a randomly selected class lasts for 47 minutes or less is 0.
**Interactive Component:**
Students can input their values and check answers interactively.
**Next Steps:**
* [Next Question](#)
This example illustrates the key concepts of continuous uniform distributions and their computations through an easily understandable problem context.
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