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 percent 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 percent of production, the bonus will be paid on how many units or more?

Answer 1

Solution:
Given that,
μ = 4000, σ=60
By using standard normal distribution ,we have to find the corresponding z-values as
P( Z> z)= 5%
1-p( Z=< z)= 0.05
p( Z=< z)= 0.95
From the standard normal table.
P( Z< 1.645 )= 0.95
z= 1.645
Now using the z-score formula, we can find the value of x as follows,
z=(x- μ)/σ
z×σ=( x- μ)
x= μ+( z×σ)
x=4000 + [(1.645)×60]
=4000 + 98.7
x=4098.7
x= 4099

The bonus Will be paid on 4099 units or more.