Homework Help is Here – Start Your Trial Now!
Math
Statistics
Consider a binomial distribution with 15 trials. Look at a table showing binomial probabilities for various values of p, the probability of success on a single trial. For what value of p is the distribution symmetric?

Consider a binomial distribution with 15 trials. Look at a table showing binomial probabilities for various values of p, the probability of success on a single trial. For what value of p is the distribution symmetric?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Please answer this. Show work!
## Analyzing Symmetry in Binomial Distributions Consider a binomial distribution with 15 trials. Look at a table showing binomial probabilities for various values of \( p \), the probability of success on a single trial. For what value of \( p \) is the distribution symmetric? ### Options: - \( p = 0.10 \) - \( p = 0.05 \) - \( p = 0.50 \) - \( p = 0.85 \) - \( p = 0.01 \) ### Explanation: For a binomial distribution to be symmetric, the probability of success \( p \) should be \( 0.50 \). This value means that the chances of success and failure are equal, leading to a balanced and symmetric probability distribution around the mean. **Graph Explanation:** If a graph or table illustrating binomial probabilities for various values of \( p \) and 15 trials were present: - When \( p = 0.50 \), the bar heights on the left and right sides of the mean (number of successes) would be mirror images of each other, indicating symmetry. - For values of \( p \) significantly different from 0.50, such as 0.10, 0.05, 0.85, or 0.01, the distribution would be skewed either to the left or right, resulting in an asymmetric shape. In conclusion, the distribution is symmetric for \( p = 0.50 \).
Transcribed Image Text:## Analyzing Symmetry in Binomial Distributions Consider a binomial distribution with 15 trials. Look at a table showing binomial probabilities for various values of \( p \), the probability of success on a single trial. For what value of \( p \) is the distribution symmetric? ### Options: - \( p = 0.10 \) - \( p = 0.05 \) - \( p = 0.50 \) - \( p = 0.85 \) - \( p = 0.01 \) ### Explanation: For a binomial distribution to be symmetric, the probability of success \( p \) should be \( 0.50 \). This value means that the chances of success and failure are equal, leading to a balanced and symmetric probability distribution around the mean. **Graph Explanation:** If a graph or table illustrating binomial probabilities for various values of \( p \) and 15 trials were present: - When \( p = 0.50 \), the bar heights on the left and right sides of the mean (number of successes) would be mirror images of each other, indicating symmetry. - For values of \( p \) significantly different from 0.50, such as 0.10, 0.05, 0.85, or 0.01, the distribution would be skewed either to the left or right, resulting in an asymmetric shape. In conclusion, the distribution is symmetric for \( p = 0.50 \).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS