# central limit theorem

1. ### CLT Chi squared and negativity

A variable with the number of degrees of freedom reaching infinity has a distribution coinciding with normal distribution (as CLT). On the other hand, this variable cannot take negative values. How to explain it? Is there an assumption in CLT that it can be used for positive values only?
2. ### Help with R code to produce proportions of sample means above one sigma

Hi everyone, I'm struggling with the following question for an R assignment: Demonstrate understanding of the Central Limit Theorem, using R, by showing how the distribution of the sample mean changes according to sample size. Consider a Poisson distribution with λ = 1.5. Generate samples of...
3. ### Why One Sample For Confidence Intervals?

As I understand it, The Central Limit Theorem and Confidence Intervals are related. What is the best way to explain why the Confidence Interval formula uses only one sample whereas the Central Limit Theorem uses 'many' samples? Isn't the x-bar in the CI formula the mean of one sample? Don't we...
4. ### Central Limit Theorem Indicative of Underlying Distribution?

Hi All, I've been reading threads off and on for a couple days, and I can't get a good feel for how to answer this question I've got stuck in my head. I'm sure the answer is in here, but I'm an engineer, not a statistician, so I can't make the leap to apply the posts I've read to the...
5. ### How does the Central Limit Theorem explain the empirical rule? student question

How does the Central Limit Theorem explain the empirical rule? engineering student in need of some conceptual assistance? thanks
6. ### stuck with this problem!!!! need help

The minimum force required to break a particular type of cable is normally distributed with mean 12,432 and standard deviation 25. A random sample of 400 cables of this type is selected. Calculate the probability that at least 349 of the selected cables will not break under a force of 12,400...
7. ### How to use the Z-test or T-Test given the sample of a non-normal population

Hi Everyone, I've tried my best to stay away from forums because I like to try to learn things on my own, but this is the third assignment I've had in this class and I'm baffled by it. I don't want to copy it verbatim in case the prof is watching. We are given the sample data of non-normal...
8. ### Central limit theorem effect of number of samples vs sample size

Hey guys, For an assignment I've been asked to investigate the CLT when sampling from different distributions using different sample sizes. Do to this in R, I've created histograms of the binomial, poisson, and uniform distribution each with 10, 100, 1000 samples of sample sizes of 10, 20...
9. ### Confidence intervals: normal vs t-distribution (central limit theorem)

Hi all! We did a serological survey for a disease taking 300 samples in a population of 50 000. If our sample mean gives a 2% prevalence. How do we work out the confidence intervals? I have all the formula's and there are great CI calculators on the web BUT seeing that is only one survey...
10. ### finding Confidence interval without CLT

Hi all, I searched the posts and I did not get what I wanted. so here is the question: In our Hw we are given daily sales of pastries and coffee for a shop in a semester(which is 70 days). it means I have a mean and a standard deviation for each. Knowing that coffee or pastries are 3\$ each...
11. ### Help Reviewing Central Limit Theorem Multiple Choice Questions

Hi All, Can someone help me review my answers below? This is a practice quiz and I am unable to get a good score. I am not sure which question I am getting wrong. My answers are highlighted in bold. :shakehead Question 2 An insurance company has 150,000 automobile policyholders. The...
12. ### Using central limit theorem for approximation

I am working on a past exam question and I am not so sure whether or not my answer is correct. If anybody could give me any guidance i would be most appreciated. I have attached the question and my solution in a jpeg file.
13. ### Newbie question on central limit theorem and standard error

Hi all: First post here, hopefully in the right forum. I'm trying to teach myself basic stats (using the book Statistics in a Nutshell) and I'm trying to get my head round something. The book gives a brief discussion of the Central Limit Theorem, and then says that it shows...
14. ### Sample distribution of means and the minimum number of samples/population size

Hi, Im having some issues with 2 things, and would appreciate it if someone could clear things up. (1) Ive read that the mean of "the sampling distribution of means" is the same as the "populations" mean. To construct the sampling distribution of means, i need to take X * number of...
15. ### Histogramms and the Central limit theorem

Hi everybody I was wondering the following: If we make histogramms for a large number of samples for any aribitrary distribution (and assume that the samples are independent) - will the histogramm look more and more like a normal distribution for a larger number of samples? I was wondering...
16. ### Central limit theorem, confusion over sample size.

Good morning, Im having some issues getting my head around the sample size of the central limit theorem. Eg Thirty random observation are taken from each of the following distributions and the sample mean is calculated. Find the probability that the sample mean exceeds 5 given that X is the...
17. ### A question on central limit theorem

Hi I have a quick question on central limit theorem. I am missing something obvious so hoping someone can help. If we had a sample set of say a million observations, and all of them had the same value, say 10. Then every sample that you draw from this set of size 30 or more, will...