# What does the central limit theorem tell us about the probability distribution?

## What does the central limit theorem tell us about the probability distribution?

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In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population’s actual distribution shape.

## How do you explain the central limit theorem?

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed.

**What three things does the central limit theorem tell us?**

Ltd. Central limit theorem (CLT) is commonly defined as a statistical theory that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

**What does the central limit theorem tell us quizlet?**

Central Limit Theorem (CLT) tells us that for any population distribution, if we draw many samples of a large size, nn, then the distribution of sample means, called the sampling distribution, will: Be normally distributed.

### Which of the following is true regarding the central limit theorem?

d. The Central Limit Theorem states that the sampling distribution of the sample mean should always have the same shape as the population distribution.

### What is the central limit theorem and why is it important in statistics?

What is the Central Limit Theorem? The CLT is a statistical theory that states that – if you take a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from that population will be roughly equal to the population mean.

**Which statement is true about the central limit theorem?**

The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.

**Does the central limit theorem apply to all distributions?**

The central limit theorem applies to almost all types of probability distributions, but there are exceptions. For example, the population must have a finite variance. That restriction rules out the Cauchy distribution because it has infinite variance.

## Why is the central limit theorem important in statistics quizlet?

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population).

## What does the central limit theorem say about the shape of the distribution of sample means quizlet?

Central Limit Theorem – As the sample size gets larger it will get closer to normal. The shape will be approximately more distributed. If the sample size is large, the sample mean will be approximately normally distributed.

**Which of the following is false about the Central Limit Theorem?**

It is false. The correct statement is: The central limit theorem states that if you have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. Thus, D is false.

**Which of the following is false about the central limit theorem?**