- CFA Exams
- CFA Level I Exam
- 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 you were told that scores on an examination were converted to standard scores with a mean of 500, range of 800, and a standard deviation of 100. A person with a score of 600 has performed better than what percentage of the persons taking the test?

A. 57 percent

B. 97.5 percent

C. 84 percent

**Explanation:**Z = (X - MU)/Standard Deviation

Z = (600 - 500)/100 = 1

Area between Z and Mean = 0.3413

Area to Left of Z = 0.5 + 0.3413 = 0.8413

Percentile Rank = 100*0.8413 = 84.13

Therefore, this person has performed better than 84% of the people who took the test.

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**User Contributed Comments**
13

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

DAS11 |
Where did they get .3413 from? |

MUSK |
More simpler way for doing this is to look for probability value (area under the curver for z=1, in one tailed test). Value is .8413 |

jam99003 |
will we have the tables for the test? it makes sense that we should, but I've not heard anything either way. |

julamo |
another super easy way to guess: around 68% of observations are within 1 standard deviation of the mean (400-600), and 32/2=16% of the scores will be below 400. 68+16=84% of the scores below 600... |

Bibhu |
Very good answer julamo. |

Kuki |
excellent julamo, i knew there had to be an easier way to do this! |

sh21 |
P.S: No table will be given in the exam. Check cfainstitute.org, (FAQS) |

NNikolaiss |
Or mean plus minus 1 st is 68 % area meaning 34% at one side. As mean is 50 % so 50+34=84 |

homersimpson |
Thanks a zillion, julamon! |

maria15 |
Where did the 68 come from? |

maria15 |
I didn't understand Julamo's shortcut. I understood analystnotes' explanation better :( |

GBolt93 |
68 is the observations within 1 standard deviation of the mean. You have to know the benchmark deviations. I.E. 1, 2, 3 standard deviations equate to 68%, 95%, 99.8% of obersavations for a 2 tailed z-test |

edrei7 |
Just remember the 68-95-99.7 rule for normal distributions. |