Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P61, the 61-percentile. This is the temperature reading separating the bottom 61% from the top 39%. P61 = C Submit Question
Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P61, the 61-percentile. This is the temperature reading separating the bottom 61% from the top 39%. P61 = C Submit 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
Related questions
Question
![### Educational Module: Understanding Percentiles in Normal Distribution
**Problem Statement:**
Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find \( P_{61} \), the 61-percentile. This is the temperature reading separating the bottom 61% from the top 39%.
\[ P_{61} = \_\_\_\_\_\_^\circ C \]
**Instructions:**
1. To find \( P_{61} \), you need to determine the z-score that corresponds to the 61st percentile in the standard normal distribution.
2. Utilize z-tables or standard normal distribution calculators to find the z-score.
3. Convert the z-score to the actual temperature using the mean and standard deviation.
**Submit Answer:**
There is a submission box followed by the unit (°C) to input the calculated percentile value and a "Submit Question" button to record your answer.
**Explanation of Graphs and Diagrams:**
- No specific graphs or diagrams are present in this problem statement. In a typical normal distribution graph, the area to the left of the 61-percentile would be shaded to represent the 61% of the data.
The known parameters:
- Mean (μ) = 0°C
- Standard Deviation (σ) = 1.00°C
By solving, you can better understand the application and concept of percentiles in the normal distribution which is essential in statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77379e33-cd78-4bf1-a88e-5489bb4fa9c3%2F2757a158-80be-4d08-adb4-a224a84df1ab%2F204eh9f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Module: Understanding Percentiles in Normal Distribution
**Problem Statement:**
Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find \( P_{61} \), the 61-percentile. This is the temperature reading separating the bottom 61% from the top 39%.
\[ P_{61} = \_\_\_\_\_\_^\circ C \]
**Instructions:**
1. To find \( P_{61} \), you need to determine the z-score that corresponds to the 61st percentile in the standard normal distribution.
2. Utilize z-tables or standard normal distribution calculators to find the z-score.
3. Convert the z-score to the actual temperature using the mean and standard deviation.
**Submit Answer:**
There is a submission box followed by the unit (°C) to input the calculated percentile value and a "Submit Question" button to record your answer.
**Explanation of Graphs and Diagrams:**
- No specific graphs or diagrams are present in this problem statement. In a typical normal distribution graph, the area to the left of the 61-percentile would be shaded to represent the 61% of the data.
The known parameters:
- Mean (μ) = 0°C
- Standard Deviation (σ) = 1.00°C
By solving, you can better understand the application and concept of percentiles in the normal distribution which is essential in statistical analysis.
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 with 1 images
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