- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 8. The Standard Normal Distribution

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**CFA Practice Question**

Suppose a set of data has a mean of 52 and a standard deviation of 6. According to Chebyshev's Theorem, at least what percentage of the data lies between 40 and 64? If the data is normally distributed, about what percentage of the data lies between 40 and 64, according to the Empirical Rule?

B. 75%, 95%

C. 94%, 100%

A. 0%, 68%

B. 75%, 95%

C. 94%, 100%

Correct Answer: B

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**User Contributed Comments**
11

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

Pooh |
Chebyshev's inequality formula says: 1-(1/c^2). First find the standardized normal deviation: 40=52+6x or 40=52-6x; x=2 By chebyshev: 1-(1/2^2) =.75 By Empirical Rule: 95% within 2 s |

cwrolfe |
Notice that none of the answers for the empirical rule are alike and that the range is +/- 2 std. deviations...99.7%. 95% is 1.95 std. dev. Pooh |

cwrolfe |
...correction...1.96 |

bobert |
Chebychev: 75% @ 2s Empirical: 95% @ 2s Confidence Interval: 95% @ 1.96s |

Raok |
forgot chebychev formula already... |

dhess0 |
me too |

EminYus |
ya by the time i get to the next chapter, all is forgot...i guess this is what the review is for |

johntan1979 |
Chebyshev = more conservative dispersion estimate Applies to ANY probability distribution irregardless of the shape of the mound i.e. doesn?t have to be normal |

sharky7 |
@Pooh How have you calculated the standardized normal deviation? |

irapp92 |
@sharky7 Pooh found the standardized normal distribution in a sort of roundabout way.. I would just stick to finding it by using z= (X-u)/stdv Chebyshev's equation is by rule the very minimum number of observations that lie less than c standard deviations from the mean. It is far more conservative than the assumptions made by the normal distribution model. I think you just have to memorize the empirical rules and the normal distribution rules and remember that they're not the same because they come from different models. |

farhan92 |
i did 1 - 1/(52^2) and realised that was bollocks so just eliminated using the 2sd=95% |