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He offers an annual bonus of $10,000 for superior performance, $6,000 for good performance, $3,000 for fair performance, and $0 for poor performance. Based on prior records, he expects an employee to perform at superior, good, fair, and poor performance levels with probabilities 0.10, 0.20, 0.50, and 0.20, respectively. Calculate the expected value of the annual bonus amountMultiple choice question.$3,700$4,000$6,000

Question

He offers an annual bonus of 10,000forsuperiorperformance,10,000 for superior performance, 6,000 for good performance, 3,000forfairperformance,and3,000 for fair performance, and 0 for poor performance. Based on prior records, he expects an employee to perform at superior, good, fair, and poor performance levels with probabilities 0.10, 0.20, 0.50, and 0.20, respectively. Calculate the expected value of the annual bonus amountMultiple choice question.3,7003,7004,000$6,000

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Solution

To calculate the expected value of the annual bonus amount, we need to multiply each bonus amount by the probability of it occurring and then sum these values.

Here's how to do it:

  • For superior performance: 10,000∗0.10=10,000 * 0.10 = 1,000
  • For good performance: 6,000∗0.20=6,000 * 0.20 = 1,200
  • For fair performance: 3,000∗0.50=3,000 * 0.50 = 1,500
  • For poor performance: 0∗0.20=0 * 0.20 = 0

Now, add these values together: 1,000+1,000 + 1,200 + 1,500+1,500 + 0 = $3,700

So, the expected value of the annual bonus amount is $3,700.

This problem has been solved

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