A worker earns $15 per hour at a plant in China and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, the average wage for the plant is $7.50 per hour.

Question

Quizplus · Accepted Answer

If only 2.5% of all workers make a higher wage, this implies a percentile rank of 97.5%, assuming a normal distribution. Using a standard normal distribution table or calculator, we can find that the corresponding z-score is approximately 1.96.

Then, we can use the formula z = (x - mu) / sigma, where z is the z-score, x is the actual wage, mu is the average wage, and sigma is the standard deviation. Rearranging this formula, we have:

x = mu + z * sigma = $15 + 1.96 * $5 = $24.80

So the statement that only 2.5% of workers make a higher wage is not consistent with an average wage of $7.50 per hour.

A Worker Earns $15 Per Hour at a Plant in China