Salaries of workers in a factory are normally distributed with mean $48000 and standard deviation $3500 What is the minimum salary of the top 20 of workers

To find the minimum salary of the top 20% of workers, we need to find the z-score that corresponds to the 80th percentile.

Using the z-score formula:

z = (x - μ) / σ

where x is the salary, μ is the mean, and σ is the standard deviation, we can rearrange the formula to solve for x:

x = z * σ + μ

To find the z-score corresponding to the 80th percentile, we use the z-score table or a calculator. The z-score that corresponds to the 80th percentile is approximately 0.84.

Plugging in the values into the equation:

x = 0.84 * $3500 + $48000

x ≈ $4800 + $48000

x ≈ $52800

Therefore, the minimum salary of the top 20% of workers is approximately $52800