**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.

Given The population has a mean = 30 Standard deviation =8 a) If the population is…

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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