Question 1193583
**1. Define the parameters:**

* **Confidence level:** 99%
* **Margin of error (E):** 1.5 hours
* **Population standard deviation (σ):** 10 hours

**2. Find the Z-score:**

* For a 99% confidence level, the Z-score is 2.576 (found using a standard normal distribution table or calculator).

**3. Calculate the required sample size (n):**

* Use the formula: 
   n = (Z-score * σ / E)² 
* Substitute the values: 
   n = (2.576 * 10 / 1.5)² 
* Calculate: 
   n ≈ 294.81

**4. Round up:**

* Since we can't have a fraction of a student, round up the sample size to the nearest whole number.

**Therefore, a sample size of 295 community college students is required to be 99% confident that the estimate of the average number of hours worked per week is within 1.5 hours of the true population mean.**