Question

Management is considering 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 that an average of 4,000 units of a small assembly is produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more

Answer 1

Answer:

4099

Explanation:

we have mean = 4000

σ = 60 units

lets make X  = weekly production

z = X-μ/σ

z = X-4000/60

At 0.05 level of signficance, z critical value = 1.645

we put this value into the equation

$z = \frac{x-4000}{60} \\1.645 = \frac{x-4000}{60}$

we cross multiply from here

60 * 1.645 = x - 4000

98.7 = x-4000

x = 4000 + 98.7

x = 4098.7

≈ 4099

the bonus would be paid on 4099 units