Central Limit Theorem Statistics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A population is strongly right-skewed. If samples of size 100 are taken repeatedly, what does the Central Limit Theorem say about the sampling distribution of the sample mean?

Solution

  1. 1
    Step 1: With a large sample size such as n=100n = 100, the Central Limit Theorem says the sampling distribution of xห‰\bar{x} will be approximately normal.
  2. 2
    Step 2: It will still be centered at the population mean and will have spread measured by the standard error.

Answer

The sampling distribution of the sample mean will be approximately normal, centered at the population mean.
The Central Limit Theorem is powerful because it allows us to use normal-model reasoning even when the original population is not normal, as long as the sample size is large enough.

About Central Limit Theorem

The Central Limit Theorem (CLT) states that for sufficiently large sample sizes (usually nโ‰ฅ30n \geq 30), the sampling distribution of the sample mean xห‰\bar{x} is approximately normal, regardless of the shape of the original population distribution.

Learn more about Central Limit Theorem โ†’

More Central Limit Theorem Examples

Example 1 hard

A population has a right-skewed distribution with [formula] and [formula]. If we take samples of siz

Example 2 hard

Explain why the Central Limit Theorem is important for making confidence intervals.

Example 3 hard

A uniform distribution has [formula] and [formula]. For samples of size 36, what are the mean and st

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