Question

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 1 percent of production based on past experience. Past records indicate that, on the average, 4,030 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 64 units. If the bonus is paid on the upper 1 percent of production, the bonus will be paid on how many units or more?

Answer 1

Given that,

mean = = 4030

standard deviation = =64

Using standard normal table,

P(Z > z) = 1%

= 1 - P(Z < z) = 0.01

= P(Z < z ) = 1 - 0.01

= P(Z < z ) = 0.99

= P(Z <2.33 ) = 0.99

z = 2.33 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 2.33*64+4030

x= 4179.12

x=4179