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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

User ChaoS Adm
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1 Answer

3 votes

Answer:

4099

Step-by-step 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 = (x-4000)/(60) \\1.645 = (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

User Soilworker
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