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Grant may get a bonus next year of $150,000 if he achieves the greatest number of house sales in his employer's real estate business
Grant may get a bonus next year of $150,000 if he achieves the greatest number of house sales in his employer's real estate business. If he comes second he will only get a bonus of $50,000 and if he doesn't come in the top two, he gets nothing. There is a 40% chance Grant gets first place, a 40% chance he gets second and a 20% chance he ranks below second place. What is the standard deviation of the bonus? (Round to the nearest dollar). Select one: A. $48,166 B. $60,000 C. $80,000 D. $75,000
Expert Solution
The formula for standard deviation with various probabilities is
σ = (Σp( X- x?)2)1/2
Where σ is the standard deviation
P is the various probabilities
X is outcomes at various probabilities
x? is the mean . Here x? = Σpx
We can tabulate the required data as per the below table.
Here x? = 40% * 1,50,000 + 40% * 50,000 + 20% * 0 = 80,000
| Place | Probability | Bonus | ( X-x?)2 | P*( X-x?)2 |
| P | X | |||
| 1 | 40% | 1,50,000 | 4,90,00,00,000 | 1,96,00,00,000 |
| 2 | 40% | 50,000 | 90,00,00,000 | 36,00,00,000 |
| 3 or more | 20% | - | 6,40,00,00,000 | 1,28,00,00,000 |
Now, (Σp( X- x?)2)1/2 = (360,00,00,000)1/2
= 60,000
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