Central Limit Theorem Worksheet
Explore the Central Limit Theorem with this worksheet, covering its definition, conditions, and applications through various question types for Grade 10 students.
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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 your work where applicable.
1. Which of the following statements best describes the Central Limit Theorem?
The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population distribution.
The distribution of individual data points approaches a normal distribution as the sample size increases.
The population mean is always equal to the sample mean.
The standard deviation of the sample means is always equal to the population standard deviation.
2. What is the minimum sample size generally considered sufficient for the Central Limit Theorem to apply?
5
10
30
100
1. The mean of the sampling distribution of the sample means is equal to the .
2. The standard deviation of the sampling distribution of the sample means is called the .
3. As the sample size increases, the standard error of the mean will .
1. Explain in your own words why the Central Limit Theorem is important in statistics.
2. A population has a mean of 50 and a standard deviation of 10. If a sample of 100 is taken from this population, what will be the mean and standard deviation of the sampling distribution of the sample means?
1. The Central Limit Theorem only applies to populations with a normal distribution.
True
False
2. A larger sample size generally leads to a more accurate estimate of the population mean.
True
False
The image below illustrates a normal distribution (bell curve), which the sampling distribution of sample means approximates according to the Central Limit Theorem.
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