Suppose that x has a distribution with μ-9 and 0-4 and it is normally distributed (bell shaped). If you take many samples of size n= 15, will the sampling distribution of sam be approximately normally distributed? (Hint: Central limit Theorem) O No O Yes, since the population is normaly distributed.
Suppose that x has a distribution with μ-9 and 0-4 and it is normally distributed (bell shaped). If you take many samples of size n= 15, will the sampling distribution of sam be approximately normally distributed? (Hint: Central limit Theorem) O No O Yes, since the population is normaly distributed.
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:**
Suppose that x has a distribution with μ=9 and σ=4 and it is normally distributed (bell shaped). If you take many samples of size n=15, will the sampling distribution of sample means be approximately normally distributed? (Hint: Central Limit Theorem)
- ○ No
- ○ Yes, since the population is normally distributed
- ○ Not possible to know
**Explanation:**
This question refers to the Central Limit Theorem (CLT), which states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, typically n ≥ 30. However, if the population itself is normally distributed, even smaller sample sizes will result in a normally distributed sampling distribution of the sample means.
In this case, since the population is already normally distributed, the sampling distribution of the sample means will also be approximately normal, even with a sample size of n=15. Thus, the correct answer is:
- Yes, since the population is normally distributed.
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