- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

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**CFA Practice Question**

You are studying the finances of a life insurance company. You believe that if Company X generates at least $150 million in earnings this year, they will pay a large amount of stock into a company bonus pool. If the earnings can fall anywhere from $110 million to $165 million with equal probability, what is the likelihood they will hit the bonus pool target?

A. 27.5%

B. 27.3%

C. 26.5%

**Explanation:**This is a continuous uniform distribution, where b = $165 million and a = $110 million. F(x) = (x - a)/ (b - a) for a < x < b; F(x) = 0 for x <= a, and F(x) = 1 for x >= b. We are solving for 1 - F(150) = 1 - (150 - 110)/(165 - 110) = 1 - 40/55 = 27.3%.

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**User Contributed Comments**
3

User |
Comment |
---|---|

Kuki |
I thought of it this way... Probability of earning every million over $110m = 1/(165-110) = 1.82% Therefore, to hit the bonus pool target, you will need anything above $150m to $165m (at the most) = $15m max. Therefore probability of achieving the target is 15*1.82% = 27.3% Hope i made sense! |

pochuevalex |
My calcs were much alike Kuki's 165-110=55 mio 165-150=15 mio 15/55=0.2727 hope that also makes sence)) |

vinoth84 |
Thanks Pochuevalex |