Central Limit Theorem Worksheet
Explore the Central Limit Theorem with this Grade 12 worksheet, covering its principle, applications, and problem-solving.
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Central Limit Theorem Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The Central Limit Theorem states that the sampling distribution of the sample mean 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 the sample means is equal to the mean.
3. The standard deviation of the sampling distribution of the sample mean is called the of the mean.
1. Which of the following conditions is NOT typically required for the Central Limit Theorem to apply?
The population must be normally distributed.
The sample size must be sufficiently large.
The samples must be randomly selected.
The observations must be independent.
2. If a population has a mean of 50 and a standard deviation of 10, what is the standard error of the mean for a sample size of 25?
0.4
2
10
50
1. Explain the practical significance of the Central Limit Theorem in statistical inference.
A certain brand of light bulb has a mean lifetime of 800 hours with a standard deviation of 60 hours. If a random sample of 36 light bulbs is selected, what is the probability that the sample mean lifetime is less than 790 hours?
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