- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 5. Binomial Distribution

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**CFA Practice Question**

It is estimated that 70% of motorists on a certain stretch of highway exceed the speed limit. A highway patrolman with a radar device randomly selects 15 motorists on this part of the highway and checks their speed. What is the probability that at least 13 are caught speeding?

A. 0.092

B. 0.128

C. 0.908

**Explanation:**We use the binomial distribution with n = 15 and pai = 0.7 to get P(X>= 13) = p(13) + p(14) + p(15) = 0.092 + 0.031 + 0.005 = 0.128.

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**User Contributed Comments**
9

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

haarlemmer |
My caculation shows that the answer is 0.1268, hehe. Afterall, it is the nearest. |

dimos |
The key is "at least" |

chamad |
how to get p(13)=0.092?...thanks |

Yurik74 |
Chamad: [15!/(13!*2!)]*(.7^13)*(.3^2) |

Sebgati |
or 15C13 * 0.7^13 * 0.3^2 |

boddunah |
messed it up on calculation part. dang it |

enetis |
on the exam these calcs would take at 3-4 valuable minutes.... tough call. |

birdperson |
enetis: it shouldnt take that long... 15C13 * (.7)^13 * (.3)^2 + 15C14 * (.7)^14 * (.3)^1 + 15C15 * (.7)^15 * (.3)^0 there are even some ways to take shortcuts in there... good luck |

dbalakos |
Do not do all the calculations. Find that P(13) = 0.092, so you already know that answer A is not correct. Multiply 0.092 with 3 and you will find something larger than 0.128 and smaller than 0.908. So, you have found the right answer the smaller one, B. |