A random variable, X, is not normally distributed, and a random sample of size n is observed. Because of the Central Limit Theorem, we can assume that the sample mean, , will be approximately normally distributed if (select all that apply):
A random variable, X, is not normally distributed, and a random sample of size n is observed. Because of the Central Limit Theorem, we can assume that the sample mean, , will be approximately normally distributed if (select all that apply):
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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Could someone please help explain this to me? I have gotten the question wrong twice now. I reviewed the Central Limit Theroem and thought I was on the right track for the question but it appears I don't understand.
![**Central Limit Theorem and Sample Distributions**
A random variable, \( X \), is not normally distributed, and a random sample of size \( n \) is observed. Because of the Central Limit Theorem, we can assume that the sample mean, \( \bar{x} \), will be approximately normally distributed if (select all that apply):
- [ ] \( n > 30 \) (the sample size is "large").
- [ ] One can always assume the sampling distribution is normal.
- [ ] The distribution of the random variable, \( X \), has many outliers.
- [ ] The population standard deviation is known.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F067cb6a4-7024-4da6-bc87-18824c7f2426%2Fec7e906a-030f-4a41-9634-caeea9652412%2Fta2yepg_processed.png&w=3840&q=75)
Transcribed Image Text:**Central Limit Theorem and Sample Distributions**
A random variable, \( X \), is not normally distributed, and a random sample of size \( n \) is observed. Because of the Central Limit Theorem, we can assume that the sample mean, \( \bar{x} \), will be approximately normally distributed if (select all that apply):
- [ ] \( n > 30 \) (the sample size is "large").
- [ ] One can always assume the sampling distribution is normal.
- [ ] The distribution of the random variable, \( X \), has many outliers.
- [ ] The population standard deviation is known.
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