Management is considering adopting a bonus system to increase production. One su

Question

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 7 percent of production based on past experience. Past records indicate that, on the average, 4,152 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 57 units. If the bonus is paid on the upper 7 percent of production, the bonus will be paid on how many units or more?

Explanation / Answer

Question on Z-score

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 7 percent of production based on past experience. Past records indicate that, on the average, 4,152 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 57 units. If the bonus is paid on the upper 7 percent of production, the bonus will be paid on how many units or more?

Solution:

Here, we have to find the number of units for the upper 7 percent of the production. We are given,

Distribution of production follows approximate normal distribution.

Mean = 4152

Standard deviation = 57

The formula for the upper score is given as below:

X = Mean + Z*SD

Now, we have to find the z value for upper 7 percent or lower 93 percent.

Z = 1.475791

Now, plug all values in the above formula given as below:

X = 4152 + 1.475791*57

X = 4236.12

Required answer = 4236 units or more

Bonus will be paid on 4236 units or more.

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