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

###
**CFA Practice Question**

For the MRC test, with scores normally distribution with m = 70 and s = 5, the cutoff for the bottom 10% is ______.

B. 68.72

C. 63.6

A. 60

B. 68.72

C. 63.6

Correct Answer: C

We start by looking in the middle of the table for 0.1. The row and column values are -1.2 and 0.08. So, the x-score that is 1.26 standard deviations below the mean cuts off the bottom 10%. This x-score, 70 - 1.28(5), is 63.6. Note that P(x < 63.6) = 0.1.

###
**User Contributed Comments**
11

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

kaliokale |
See, even analyst needs to use the a table |

RichardWang |
We just need to remember some key numbers: 68% falls within 1 standard deviation -/+ mean; 95% falls within 2 standard deviation -/+ mean. Thus bottom 10% cut off will be more than 1 standard deviation and less than 2 standard deviation under mean. Only Answer C falls into this range. (Answer A is 2 standard deviation under mean - too far; Answer B is less than 1 deviation under meam - too little.) |

tanyak |
Also, how about 70*.9 = 63 - would that work? |

Rotigga |
We know that 80% CI is 1.282 std devs from the mean. Which means two tails, each with 10%. You should memorize the 80% CI of 1.282: 70-5*1.282=63.59 |

MBandekar |
the bottom point is 70-5 = 65 10% of this is 6.5 therefore the bottom 10% cutoff is 70-6.5=63.5... This is approach right?? |

chamad |
Rottiga approach is saver..Not sure about MBandekar's! can you elaborate your approach? |

Yurik74 |
Rottiga - I love that assumption that we know 80%CI is 1.282! I just love it : ))) Seriously |

Yurik74 |
tanyak & MBandekar - no, wrong approach, checked with other m and s, global discrepency |

sgossett86 |
normal dist 90% confidence 1.68 we need 80% confidence so i did -(8/9)*(1.68)*(5)+70 to ballpark it |

degosan9 |
Totally lost on this one even with everyone's comments |

siancolli |
80% of the data lies between -1.28 and 1.28 standard deviations from the mean. The question is referring to the bottom 10% (-1.28 standard deviations from the mean). So using the z formula: [-1.28*5] + 70 = 63.6 |