The problem you're asking involves finding percentages and counts of workers within certain wage ranges, assuming a normal distribution. Here's how to approach each part:

Given:

• Mean wage (μ) = Rs. 1200
• Standard deviation (σ) = Rs. 400
• Total number of workers (N) = 6000

a. Percentage of workers getting wages above Rs. 1600

To solve this, we use the z-score formula: $z = \frac{x - \mu}{\sigma}$ where:

• $x$ = 1600 (the wage we're interested in)
• $\mu$ = 1200 (mean)
• $\sigma$ = 400 (standard deviation)

Substituting values: $z = \frac{1600 - 1200}{400} = \frac{400}{400} = 1$

From standard normal distribution tables, the area to the left of $z = 1$ is approximately 0.8413. Therefore, the area (or percentage) to the right (wages above Rs. 1600) is: $1 - 0.8413 = 0.1587 \text{ or } 15.87\%$

b. Number of workers getting wages between Rs. 600 and Rs. 900

We calculate the z-scores for Rs. 600 and Rs. 900.

For Rs. 600: $z = \frac{600 - 1200}{400} = \frac{-600}{400} = -1.5$ For Rs. 900: $z = \frac{900 - 1200}{400} = \frac{-300}{400} = -0.75$

Using the z-table:

• The area to the left of $z = -1.5$ is approximately 0.0668.
• The area to the left of $z = -0.75$ is approximately 0.2266.

The percentage of workers earning between Rs. 600 and Rs. 900 is the difference between these two areas: $0.2266 - 0.0668 = 0.1598 \text{ or } 15.98\%$ The number of workers is: $0.1598 \times 6000 = 959 \text{ workers}$

c. Number of workers getting wages between Rs. 1100 and Rs. 1500

For Rs. 1100: $z = \frac{1100 - 1200}{400} = \frac{-100}{400} = -0.25$ For Rs. 1500: $z = \frac{1500 - 1200}{400} = \frac{300}{400} = 0.75$

Using the z-table:

• The area to the left of $z = -0.25$ is approximately 0.4013.
• The area to the left of $z = 0.75$ is approximately 0.7734.

The percentage of workers earning between Rs. 1100 and Rs. 1500 is: $0.7734 - 0.4013 = 0.3721 \text{ or } 37.21\%$ The number of workers is: $0.3721 \times 6000 = 2233 \text{ workers}$

Summary:

• a. Percentage of workers getting wages above Rs. 1600: 15.87%
• b. Number of workers getting wages between Rs. 600 and Rs. 900: 959 workers
• c. Number of workers getting wages between Rs. 1100 and Rs. 1500: 2233 workers

Would you like more details or have any questions?

Here are five related questions to explore further:

1. How would the percentages change if the standard deviation was larger or smaller?
2. How can you calculate wages for a different percentile, like the 90th percentile?
3. What if wages followed a skewed distribution rather than a normal one?
4. How can you estimate the probability for any arbitrary wage using the z-score?
5. How do different confidence intervals affect the precision of wage estimates?

Tip: When using z-scores, always remember the direction you're interested in: above or below the given wage level!