- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 5. The Binomial Distribution

###
**CFA Practice Question**

For X, a binomial random variable with N = 70 and p = 0.3, we can approximate P(X < 19) by using a normal distribution with ______.

B. mean 21 and standard deviation 3.83

C. mean 70 and standard deviation 3.83

A. mean 70 and standard deviation 0.3

B. mean 21 and standard deviation 3.83

C. mean 70 and standard deviation 3.83

Correct Answer: B

We can approximate the binomial with a normal distribution because Np = 21 is greater than 5 and N(1 - P) = 49 is greater than 5. The normal distribution that we use to do the approximation has mean = Np = 21 and a standard deviation square root of N(p)(1 - p), in this case, 3.83 (to the nearest 0.01).

###
**User Contributed Comments**
9

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

mtcfa |
What the heck does "5" have to do with anything??? |

grantw |
The common rule is that you can approximate the binomial with the normal when np and n(1-p) both exceed some magic number. That magic number is variously stated as 5, 10 or 15, depending on the conservative nature of the statistician, the higher the magic number, the more conservative the statistician. From http://www.andrews.edu/~calkins/math/webtexts/prod09.htm |

TammTamm |
mtcfa, those are my same sentiments. LOL I hate Quant Methods, this is a bunch of bunk if you ask me. Anywho, that's my .02cents. |

magicchip |
Captain Kirk said "Make it so.." |

rsanfo |
Actually, Captain Picard said "Make it so...". Captain Kirk said "How many women on this planet do I get to kiss?". |

poomie83 |
Does anyone know the magic number the cfa wants us to use? |

fanDango |
42 |

FozzeyBear |
this some stupid stuff |

ashish100 |
It's complex. 42 explains it perfectly tho. |