Central Limit Theorem Worksheet
This worksheet covers key concepts of the Central Limit Theorem, including sampling distributions, sample means, and its application to various scenarios for Grade 11 students.
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Central Limit Theorem Worksheet
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Read each question carefully and provide your best answer. Show all your work for calculations.
1. The Central Limit Theorem states that the distribution of sample means approaches a distribution as the sample size increases, regardless of the shape of the population distribution.
2. When applying the Central Limit Theorem, the mean of the sampling distribution of sample means is equal to the mean (μ).
3. The standard deviation of the sampling distribution of sample means is called the of the mean.
1. Which of the following conditions is NOT required for the Central Limit Theorem to apply?
The population distribution must be normal.
The sample size must be sufficiently large.
Samples must be randomly selected.
The population variance must be finite.
2. If a population has a mean (μ) of 50 and a standard deviation (σ) of 10, what is the standard error of the mean for a sample of size 25?
0.4
2
10
50
1. A population has a mean of 100 and a standard deviation of 15. If random samples of size 36 are taken from this population, what will be the mean and standard deviation of the sampling distribution of the sample means?
2. Explain in your own words why the Central Limit Theorem is important in statistical inference.
1. The Central Limit Theorem can only be applied if the original population distribution is normal.
True
False
2. As the sample size increases, the standard error of the mean decreases.
True
False
The average weight of a certain type of apple grown in an orchard is 150 grams with a standard deviation of 10 grams. If a random sample of 64 apples is picked, what is the probability that the sample mean weight will be between 148 and 152 grams?