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Let's break down the information given in this question:

### Given Information:
1. **Mean Salary (μ):** R10,850
2. **Standard Deviation (σ):** R2,950
3. The salaries are symmetrically distributed, implying a normal distribution.
4. **Distribution Details:**
   - 68% of the salaries lie within one standard deviation (μ ± σ).
   - 96% of the salaries lie within two standard deviations (μ ± 2σ).
   - 100% of the salaries lie within three standard deviations (μ ± 3σ).

### Questions:
1. **(1) What is the salary of the highest-paid employee(s) in the company?**
   - In a normal distribution, the highest salary would be at the mean plus three standard deviations (μ + 3σ).
   - Calculation:  
     \[
     \text{Highest Salary} = \mu + 3\sigma = 10,850 + 3 \times 2,950
     \]
     \[
     = 10,850 + 8,850 = 19,700
     \]
   - Therefore, the highest-paid employee(s) earn **R19,700**.

2. **(2) Determine the percentage of employees who do not earn a living wage.**
   - A living wage is stated as R4,950 per month.
   - We need to find the percentage of employees earning less than R4,950.
   - To find this percentage:
     - First, find how many standard deviations R4,950 is from the mean:
     \[
     z = \frac{4,950 - 10,850}{2,950} = \frac{-5,900}{2,950} = -2
     \]
   - A z-score of -2 indicates that R4,950 is two standard deviations below the mean.
   - In a normal distribution:
     - The percentage of data within two standard deviations from the mean (both directions) is 96%.
     - This means 4% lie outside this range (2% below -2σ and 2% above +2σ).
   - Therefore, the percentage of employees earning **less than R4,950** (below -2σ) is **2%**.

### Summary of Answers:
1. The salary of the highest-paid employee(s) in the company is **R19,700**.
2. The percentage of employees who do not earn a living wage is **2%**.

Would you like more details or have any questions about this solution?

### Further Questions for Exploration:
1. What percentage of employees earn more than R16,000?
2. How many employees earn between R7,900 and R13,800?
3. What is the median salary in this distribution?
4. How does the standard deviation impact the salary distribution?
5. What is the range of salaries that 68% of employees fall into?

### Tip:
In a normal distribution, understanding the mean and standard deviation helps you quickly assess the spread and central tendency of the data.

A company did an analysis of the salary structures of its employees. The mean salary is R10,850 with a standard deviation of R2,950. 68% of monthly salaries lie within one standard deviation of the mean, 96% within two standard deviations, and 100% within three. Employees need at least R4,950 to make a living wage. 1) What is the salary of the highest-paid employee(s)? 2) Determine the percentage of employees who do not earn a living wage.

This problem covers salary distribution analysis using a normal distribution. It includes calculating the highest-paid employee's salary and determining the percentage of employees earning below a living wage. Suitable for students in Grades 10-12.

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