Question

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 amount

Answer 1

If 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. The expected value of the annual bonus amount will be: $3,700

First step

Expected value for Superior performance=$10,000×0.10

Expected value for Superior performance=$1,000

Expected value for Good performance=$6,000×0.20

Expected value for Good performance=$1,200

Expected value for Fair performance=$3,000×0.50

Expected value for Fair performance=$1,500

Expected value for Poor performance=$0×`1,500

Expected value for Poor performance=$0

Now let determine the total  expected value of the annual bonus amount

Expected value of annual bonus amount=$1,000+$1,200+$1,500+$0

Expected value of annual bonus amount=$3,700

Inconclusion if 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. The expected value of the annual bonus amount will be: $3,700

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