Management is considering a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate that an average of 4,000 units of a small assembly is 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% 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

Question

Quizplus · Accepted Answer

To find the number of units for the upper 5% of production, we use the z-score formula for a normal distribution. The z-score corresponding to the upper 5% (95th percentile) is approximately 1.645. The formula to calculate the value is: X = μ + (Z * σ), where μ is the mean, Z is the z-score, and σ is the standard deviation. Plugging in the values: X = 4000 + (1.645 * 60) = 4000 + 98.7 ≈ 4099. Therefore, the bonus would be paid on 4099 units or more.

Management Is Considering a Bonus System to Increase Production