Estimating the Lowest Hourly Wages of the 100 Highest Paid Workers

To estimate the lowest hourly wages of the 100 highest paid workers, we need to consider the normal distribution of the hourly wages of the entire population of workmen. Here are the steps to estimate the lowest hourly wages:

Gather Information
- Mean (μ) of hourly wages = Rs 70
- Standard deviation (σ) of hourly wages = Rs 5
- Total number of workmen = 1000

Identify the Z-Score
The Z-score is a measure of how far a particular data point is from the mean in terms of standard deviations. We can use the Z-score formula to estimate the Z-score for the 100th highest paid worker.

Z = (X - μ) / σ

Calculate Z-Score
Using the formula, we can calculate the Z-score for the 100th highest paid worker:

Z = (X - 70) / 5

To estimate the lowest hourly wage of the 100th highest paid worker, we need to find the Z-score that corresponds to the 99th percentile. This can be done using a standard normal distribution table or statistical software.

Find Z-Score for the 99th Percentile
The 99th percentile corresponds to a Z-score of approximately 2.33. This means that the hourly wage of the 100th highest paid worker is approximately 2.33 standard deviations above the mean.

Calculate Estimated Lowest Hourly Wage
To estimate the lowest hourly wage of the 100th highest paid worker, we can use the Z-score and the formula:

X = Z * σ + μ

Substituting the values, we get:

X = 2.33 * 5 + 70
X ≈ 81.65

Therefore, the estimated lowest hourly wage of the 100 highest paid workers is approximately Rs 81.65.

Conclusion
In this estimation, we assumed that the distribution of hourly wages is normal, which is a common assumption in statistical analysis. By using the Z-score and the known mean and standard deviation, we were able to estimate the lowest hourly wage of the 100th highest paid worker. It is important to note that this estimation is based on the assumption of a normal distribution and may not be exact in reality. However, it provides a reasonable estimate based on the given information.