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) 6255
B) 5120
C) 3196
D) 4099

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 for a z-score: z = (X - μ) / σ, where μ = 4000 and σ = 60, we solve for X: 1.645 = (X - 4000) / 60. Solving for X gives X ≈ 4099.

Management Is Considering Adopting a Bonus System to Increase Production