Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?
A) 6,255
B) 5,120
C) 3,196
D) 4,099
E) None of the choices are correct

Question

Quizplus · Accepted Answer

To find the number of units for the top 5% of production, we need to find the z-score that corresponds to the 95th percentile of a standard normal distribution, which is approximately 1.645. Using the formula: X = μ + zσ, where μ = 4000 and σ = 60, we calculate X = 4000 + (1.645)(60) = 4,099.

Management Is Considering Adopting a Bonus System to Increase Production