- 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**

Given that X is a binomial random variable, with N = 5 and p = 0.3 and that we want to find P(X < 3), which of the following is true?

B. We can approximate P(X < 3) using a normal with mean = 1.5 and standard deviation = 1.02.

C. We cannot approximate this binomial distribution with a normal distribution.

A. We can approximate P(X

_{B}< 3) with P(X_{N}< 2.5).B. We can approximate P(X < 3) using a normal with mean = 1.5 and standard deviation = 1.02.

C. We cannot approximate this binomial distribution with a normal distribution.

Correct Answer: C

To approximate the binomial with a normal distribution, Np and N(1 - p) must both be greater than 5. Here, Np = (5)(0.3) = 1.5, which is not greater than 5. So, we cannot approximate P(X < 3) using a normal distribution [we would use a binomial table to find P(X < 3)].

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**User Contributed Comments**
7

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

yanpz |
Why "to approximate the binomial with a normal distribution, Np and N(1-p) must both be greater than 5"? |

whiteknight |
Also...why should we try to approximate the binomial with a normal distribution ? |

bahodir |
Since NP and N(1-P) are greater than 5 means that N is a big number, we can somehow assume that the error from sampling is insignificant. Doing so, the shape of the your distribution may be similar to normal distribution |

bahodir |
You may ask "why 5?" It is a kind of convention, I guess. |

StanleyMo |
Please refer here for more details: http://en.wikipedia.org/wiki/Binomial_distribution |

pranit |
Thank you StanleyMo. That was of great help. |

johntan1979 |
Only if N > 30, then normal distribution. Not sure where the Np and N(1-p) >5 comes from. |