Question

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 2 percent of production based on past experience. Past records indicate that, on the average, 4,472 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 69 units. If the bonus is paid on the upper 2 percent of production, the bonus will be paid on how many units or more?

Answer 1

Answer:

To determine the X value

Given,

Mean = 4472

Standard deviation = 69

P( Z > z) = 0.02

Z(0.02) = 2.0537 (since from critical value table)

Now consider,

Z = (X - )/

X = + Z ()

X = 4472 + 2.0537(69)

X = 4472 + 141.7053

X = 4613.7053

X = 4614 units

Hence the bonus will be paid on atleast 4614 units