deviation ofo = 8. a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample ofn b. If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4? c. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 64? 4?
deviation ofo = 8. a. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample ofn b. If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 4? c. If the population distribution is normal, what is the probability of obtaining a sample mean greater than M = 32 for a sample of n = 64? 4?
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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Transcribed Image Text:**Question 16: Understanding Probability in Different Distributions**
A population has a mean (\(\mu\)) of 30 and a standard deviation (\(\sigma\)) of 8. Consider the following scenarios:
a. **Normal Distribution with Small Sample Size:**
- If the population distribution is normal, what is the probability of obtaining a sample mean greater than \(M = 32\) for a sample of \(n = 4\)?
b. **Positively Skewed Distribution with Small Sample Size:**
- If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than \(M = 32\) for a sample of \(n = 4\)?
c. **Normal Distribution with Large Sample Size:**
- If the population distribution is normal, what is the probability of obtaining a sample mean greater than \(M = 32\) for a sample of \(n = 64\)?
d. **Positively Skewed Distribution with Large Sample Size:**
- If the population distribution is positively skewed, what is the probability of obtaining a sample mean greater than \(M = 32\) for a sample of \(n = 64\)?
Explore how the characteristics of the distribution and the sample size influence the probability of obtaining a specific sample mean.
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