Question

2. Suppose a paint manufacturer has a daily production, x, that is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons. Management wants to create an incentive bonus for the production crew when the daily production exceeds the 90th percentile of the distribution, in hopes that the crew will, in turn, become more productive. At what level of production should management pay the incentive bonus?

Answer 1

Solution :

Given that,  

mean = = 100000

standard deviation = = 10000

Using standard normal table ,

P(Z > z) = 90%

1 - P(Z < z) = 0.9

P(Z < z) = 1 - 0.9

P(Z < -1.282) = 0.1

z = -1.282

Using z-score formula,

x = z * +

x = -1.282 * 10000 + 100000 = 87180

At level of production should management pay the incentive bonus is 87180