- 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**

The distribution of lifetimes for a certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the 33rd percentile of the distribution of lifetimes.

A. 560

B. 1044

C. 956

**Explanation:**P(z<=?) = 0.33

z = -0.44

-0.44 = (x-1000)/(100)

x = -44 + 1000 = 956

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**User Contributed Comments**
10

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

labsbamb |
how we found .44? |

Janey |
If you look in the -ve z table for .33 you will see it comes under row -.40 and column.04 (.44) |

dimanyc |
you can look at the z-table as much as you want, only you won't see it at the exam. |

Xocrevilo |
Janey, why did you use those parameters for getting that z-score?! Logically, we know that the 33rd percentile is below the mean (so below 1000). As the s.d. is only 100, then one would expect the 33rd percentile to be quite close to the 50th percentile (i.e. the mean, 1000), which suggests that 956 is the only answer. |

aakash1108 |
0.33 = 1 - 0.67 ->0.33 = 1 - F(0.44) ->0.33 = 1- P(Z<=0.44) ->0.33 = P(Z<=-0.44) also; P(Z<=-0.44)=P(Z<=(x-1000)/100) solving for x. -> -0.44 = (x-1000)/100 -> -44 = x - 1000 -> x = -44 + 1000 -> x = 956 I hope this clears! |

Yfj211 |
Same logic as Xocrevilo |

petervinh18 |
Are there any other way to do this problem without look into chart-table (since we cannot use the chart on the exam). |

ColonelCFA |
I used common sense. A SD in each direction encompasses roughly 68% of the distribution. Half it to get the percentage below the mean. AKA the 100 below the mean is 34%. The mean = 50%. So at 900 the percentile is 50-34=16%, well below the 33% we are looking for. So 33% must be >900 and <1000 leaving only option C. |

jjhigdon |
Also don't know how one would know the Z score without having the table. I used the same logic as ColonelCFA and Xocrevilo: Ballpark how far below the mean the 33% is in terms of #standard deviations and use process of elimination for the answers. |

SFait79 |
1. the 33 percentile can't be above the average (exclude B) 2. 560 is MORE THAN 4 SD BELOW the mean, which is almost zero (exclude A) ---> only C makes sense. |