A community for students.
Here's the question you clicked on:
 0 viewing
purplemouse
 2 years ago
What conditions must be fulfilled to apply the Central Limit Theorem? And in what cases would it be applied?
purplemouse
 2 years ago
What conditions must be fulfilled to apply the Central Limit Theorem? And in what cases would it be applied?

This Question is Closed

kropot72
 2 years ago
Best ResponseYou've already chosen the best response.0The Central Limit Theorem states that, provided n (the number in the sample) is at least 30, the distribution of sample means is Normal, no matter what the distribution of the population from which the sample was taken. This theorem justifies the use of confidence intervals for sample means and proportions.

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.0Not exactly n at least 30, that would still be the "t" distribution (already close to Normal for n = 30), but the limit as n> infinity for sample means is Normal.

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.0You're also only supposed to use Normal if you know the population variance (st. deviation).,

kropot72
 2 years ago
Best ResponseYou've already chosen the best response.0If X bar is the mean of a sample size n from a population which is not Normally distributed, then the Central Limit Theorem states that X bar will be approximately Normally distributed if the sample size is sufficiently large.\[(a\ common\ value\ given\ is\ n \ge30)\]

dlipson1
 2 years ago
Best ResponseYou've already chosen the best response.0Key word: "approximately". In general, use the t distribution (it's not much harder, same basic procedures), which approaches normal for larger and larger n.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.