True or False: 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

The mean wage can be calculated using the z-score formula. Given that 2.5% of workers earn more than $15, the z-score is approximately 1.96 (for the upper tail of a normal distribution). Using the formula $ z = \frac{X - \mu}{\sigma} $, where $ X = 15 $, $ \sigma = 5 $, and $ z = 1.96 $, solving for $ \mu $ gives a mean wage of approximately $5.20, not $7.50.

True or False: a Worker Earns $15 Per Hour at a Plant