For a random sample of size n from a population distribution having mean μ and standard deviation o, then as the sample size increases, the sampling distribution of the sample mean x approaches an approximately binomial istribution. True False

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Question:**
For a random sample of size n from a population distribution having mean μ and standard deviation σ, then as the sample size increases, the sampling distribution of the sample mean x̄ approaches an approximately binomial distribution.

- ○ True
- ○ False

**Explanation:**  
This question relates to the concept of the sampling distribution of the sample mean and the Central Limit Theorem. The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This question asks if the distribution approaches a binomial distribution, which is typically related to binary outcomes (e.g., success/failure).
Transcribed Image Text:**Question:** For a random sample of size n from a population distribution having mean μ and standard deviation σ, then as the sample size increases, the sampling distribution of the sample mean x̄ approaches an approximately binomial distribution. - ○ True - ○ False **Explanation:** This question relates to the concept of the sampling distribution of the sample mean and the Central Limit Theorem. The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This question asks if the distribution approaches a binomial distribution, which is typically related to binary outcomes (e.g., success/failure).
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