Question

Weekly production of backup electricity generators at General Electronics Company (GEC) follows a normal distribution with a mean of μ = 4000 units per week and a standard deviation of σ = 60 units. Management at GEC is considering adopting a bonus system to increase production.

1. One suggestion is to pay a bonus to production workers on the highest 5% of production. What is the minimum production that will qualify a worker for this bonus?
2. Suppose the management would like to give a bonus to production workers on the highest 10% of production. What is the minimum production that will quality a worker for this bonus?

Answer 1

Solution :

mean = = 4000

standard deviation = = 60

a. Using standard normal table,

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05 =

P(Z < 1.65) = 0.95

z =1.65

Using z-score formula,

x = z * +

x = 1.65 * 60 + 4000

x = 4099

minimum production = 4099

b. Using standard normal table,

P(Z > z) = 10%

1 - P(Z < z) = 0.1

P(Z < z) = 1 - 0.1 = 0.9

P(Z < 1.28) = 0.9

z =1.28

Using z-score formula,

x = z * +

x = 1.28 * 60 + 4000

x = 4076.8

minimum production = 4076.8