Question

Question 5 6 pts A paint manufacturer has a daily production, x, that is normally distributed with a mean of 500,000 gallons and a standard deviation of 35,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 97th percentile in the distribution - in hopes that the crew will become more productive. At what level of production should management pay the incentive bonus? In other words, complete the following sentence. Hint, use your table to find the right Z-score then use your standard deviation and mean to calculate the amount: Management should pay an incentive bonus when a day's production exceeds gallons, i.e., is in the top 3% of the current daily production distribution

Answer 1

Mean (1) = 500,ooo gallons standard deviation (6) = 35,000 gallons Escore = X- Plze Zscov) = P(ZR X-44 ) Plz < Eslore) = 0.97 (for 97th percentile) using normal distribution Table Zscore = 1.881 X- M 1.881 To X-500,000 = 1.881 35000 x 2 565835 Management should pay a day's production an incentive bonus when exceeds | 565835 gallons