| Suppose that the readings on the thermometers are normally distributed with a mean of 0° and a standard deviation of 1.00°C. If 5% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
| Suppose that the readings on the thermometers are normally distributed with a mean of 0° and a standard deviation of 1.00°C. If 5% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
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 Statement:**
Suppose that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. If 5% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
**Solution:**
To find the temperature that separates the top 5% of thermometer readings (those that are too high and therefore rejected), we need to determine the 95th percentile of the normal distribution. The percentile can be found using the properties of the normal distribution.
Since the mean (μ) is 0°C and the standard deviation (σ) is 1.00°C, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 95th percentile.
Once the Z-score is found, the corresponding thermometer reading can be calculated using the formula:
\[ X = μ + Z \times σ \]
Where:
- \( X \) is the thermometer reading.
- \( μ \) is the mean (0°C).
- \( Z \) is the Z-score for the 95th percentile.
- \( σ \) is the standard deviation (1.00°C).
This calculation will give the temperature reading that separates the acceptable thermometer readings from the ones that are rejected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa00d0151-b5df-4ee3-a0d6-fdfba7d1c4f7%2F881db696-e175-4326-ae2f-083cad639021%2Fsxijtwt_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. If 5% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
**Solution:**
To find the temperature that separates the top 5% of thermometer readings (those that are too high and therefore rejected), we need to determine the 95th percentile of the normal distribution. The percentile can be found using the properties of the normal distribution.
Since the mean (μ) is 0°C and the standard deviation (σ) is 1.00°C, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 95th percentile.
Once the Z-score is found, the corresponding thermometer reading can be calculated using the formula:
\[ X = μ + Z \times σ \]
Where:
- \( X \) is the thermometer reading.
- \( μ \) is the mean (0°C).
- \( Z \) is the Z-score for the 95th percentile.
- \( σ \) is the standard deviation (1.00°C).
This calculation will give the temperature reading that separates the acceptable thermometer readings from the ones that are rejected.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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