Question

Management at Gordon Electronics is considering adopting 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 weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard deviation is 60 units per week. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more?

Answer 1

Solution:-

Given that,

mean = = 4000

standard deviation = = 60

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < 1.645 ) = 0.95  

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 60 + 4000

x = 4098.7

x = 4099 units or more.