Question 1192349
**A) Mean and Standard Deviation of the Average Number of Moths**

* **Mean of the sample means (Central Limit Theorem):** 
    * The mean of the sample means is equal to the population mean: 
        * Mean of sample means = 0.4 moths

* **Standard deviation of the sample means (Standard Error):**
    * Standard Error (SE) = σ / √n 
        * where:
            * σ is the population standard deviation (0.9 moths)
            * n is the sample size (60 traps)

    * SE = 0.9 / √60 
    * SE ≈ 0.116 moths

**B) Probability of the average number of moths being greater than 0.6**

* **Standardize the value 0.6:**
    * Z-score = (X - μ) / σ 
        * where:
            * X is the value we're interested in (0.6 moths)
            * μ is the mean of the sample means (0.4 moths)
            * σ is the standard deviation of the sample means (0.116 moths)

    * Z-score = (0.6 - 0.4) / 0.116 
    * Z-score ≈ 1.72

* **Calculate the probability using the standard normal distribution:**
    * We need to find P(Z > 1.72) 
        * Using a standard normal distribution table or a calculator, we find that P(Z > 1.72) ≈ 0.0427 

**Therefore:**

* **A) Mean of the average number of moths: 0.4 moths** 
* **B) Standard deviation of the average number of moths: 0.116 moths**
* **Probability that the average number of moths in 60 traps is greater than 0.6: 0.04 (or 4%)**

This analysis shows that while the average number of moths per trap is low, the probability of finding an average of more than 0.6 moths in 60 traps is relatively small (about 4%). This suggests that the overall moth population in the area may not be excessively high.