Question 1197761: A population has a skewed right distribution with mean 27 and standard deviation 12. For samples of size 40, the sampling distribution of the sample mean has shape that is , center , and standard deviation .
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! * **Shape:**
* **Approximately Normal:** Even though the population distribution is skewed right, the Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal for sufficiently large sample sizes. With a sample size of 40, the distribution is likely to be close to normal.
* **Center:**
* **27:** The mean of the sampling distribution of the sample mean is equal to the mean of the population, which is 27.
* **Standard Deviation:**
* **Standard Error of the Mean (SEM):**
* SEM = σ / √n
* SEM = 12 / √40
* SEM ≈ 1.897
**In summary:**
* The sampling distribution of the sample mean will have an **approximately normal** shape.
* The center (mean) of the sampling distribution will be **27**.
* The standard deviation of the sampling distribution (standard error) will be approximately **1.897**.
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