Central Limit Theorem Worksheet
Explore the Central Limit Theorem with this grade 9 math worksheet, covering sample means, population distributions, and the shape of sampling distributions.
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Central Limit Theorem
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Read each question carefully and answer to the best of your ability. Show all work where applicable.
1. What does the Central Limit Theorem (CLT) state about the sampling distribution of the sample mean?
It will always be identical to the population distribution.
It will be approximately normal, regardless of the population distribution, if the sample size is large enough.
It will always be skewed right.
It will have a mean of 0 and a standard deviation of 1.
2. A population has a mean (μ) of 50 and a standard deviation (σ) of 10. If samples of size n=36 are taken repeatedly, what will be the mean of the sampling distribution of the sample means (μ_x̄)?
10
50
36
1.67
3. According to the Central Limit Theorem, if the sample size is sufficiently large, the sampling distribution of the sample mean will be approximately , regardless of the shape of the population distribution.
4. The standard deviation of the sampling distribution of the sample mean is also known as the of the mean.
5. The Central Limit Theorem applies only to populations that are normally distributed.
True
False
6. A population has a mean height of 170 cm and a standard deviation of 10 cm. If a sample of 100 students is randomly selected, what is the standard error of the mean for this sample?