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 P53 P53 = (Report answer accurate to 4 decimal places.)
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 P53 P53 = (Report answer accurate to 4 decimal places.)
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
![**Problem Description:**
The lengths of a professor’s classes have a continuous uniform distribution between 49.29 minutes and 55.55 minutes. If one such class is randomly selected, find \( P_{53} \).
**Solution:**
To find \( P_{53} \), which represents the 53rd percentile of the distribution, you would use the formula for the percentile of a uniform distribution:
\[ P_k = a + \frac{k}{100} \times (b - a) \]
where:
- \( a \) is the lower limit of the distribution (49.29 minutes),
- \( b \) is the upper limit of the distribution (55.55 minutes),
- \( k \) is the percentile you wish to find (53).
**Calculation:**
\[ P_{53} = 49.29 + \frac{53}{100} \times (55.55 - 49.29) \]
**Report Answer:**
Make sure to report the answer accurate to 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96ccea39-6e20-4e83-b9fb-b22d2ae10407%2F18d6f271-3847-4741-8581-48d3268f2687%2Fxesimw_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The lengths of a professor’s classes have a continuous uniform distribution between 49.29 minutes and 55.55 minutes. If one such class is randomly selected, find \( P_{53} \).
**Solution:**
To find \( P_{53} \), which represents the 53rd percentile of the distribution, you would use the formula for the percentile of a uniform distribution:
\[ P_k = a + \frac{k}{100} \times (b - a) \]
where:
- \( a \) is the lower limit of the distribution (49.29 minutes),
- \( b \) is the upper limit of the distribution (55.55 minutes),
- \( k \) is the percentile you wish to find (53).
**Calculation:**
\[ P_{53} = 49.29 + \frac{53}{100} \times (55.55 - 49.29) \]
**Report Answer:**
Make sure to report the answer accurate to 4 decimal places.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman