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 mean wage for the plant is $7.50 per hour.

Question

Quizplus · Accepted Answer

Given that only 2.5% of all workers make a higher wage than $15 per hour, this places the $15 wage at the 97.5th percentile of a normal distribution. Using the Z-score formula, we can calculate the mean. The Z-score for the 97.5th percentile is approximately 1.96. Using the formula $Z = \frac{(X - \mu)}{\sigma}$, where $X = 15$, $\sigma = 5$, and solving for $\mu$ (the mean), we find that the mean is not $7.50. The calculation would actually increase the mean above $15, not decrease it to $7.50.

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