SOLUTION: The number of crimes committed daily has some unknown probability distribution with the mean μ = 2.8 and the standard deviation σ = 4. A random sample of n = 100 days will be t

Question 1198217: The number of crimes committed daily has some unknown probability
distribution with the mean μ = 2.8 and the standard deviation σ = 4.
A random sample of n = 100 days will be taken. Describe the distribution of the average
number (the mean number) of crimes for that sample (5 points):
a.) unknown distribution with the mean = 2.8 and the standard deviation = 0.4
b.) approximately normal distribution with the mean = 2.8 and the standard deviation = 4
c.) unknown distribution with the mean = 2.8 and the standard deviation = 4
d.) approximately normal distribution with the mean = 2.8 and the standard deviation = 0.4
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
The correct answer is:
**d.) approximately normal distribution with the mean = 2.8 and the standard deviation = 0.4**
**Explanation:**
* **Central Limit Theorem:** This theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the original population distribution, as long as the sample size is sufficiently large (typically considered to be n ≥ 30).
* **Mean of the Sampling Distribution:** The mean of the sampling distribution of the sample mean is equal to the population mean: μ_x̄ = μ = 2.8
* **Standard Deviation of the Sampling Distribution (Standard Error):**
* σ_x̄ = σ / √n
* σ_x̄ = 4 / √100
* σ_x̄ = 4 / 10
* σ_x̄ = 0.4
**Therefore, the distribution of the average number of crimes for the sample of 100 days is approximately normal with a mean of 2.8 and a standard deviation of 0.4.**

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