- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 7. The Standard Normal Distribution

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**CFA Practice Question**

For x, a random variable from a normal distribution with mean 40 and standard deviation 5, P(x > 20) = ______ (to the nearest 0.1%).

B. 95%

C. 1-

A. 0+

B. 95%

C. 1-

Correct Answer: C

The z-score for 20 is (20 - 40)/5 = -4. Reading the normal table, the smallest entry is -3.09 and its value is 0.0010. So, P(x < 20) = 0+. Thus, P(x > 20) = 1 - 0+ = 1-. That is, when rounded to the nearest 0.1%, the answer is 100%, but because 1 holds a special place in probability (indicating a must-happen event), we report 1-.

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**User Contributed Comments**
7

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

magicchip |
well, it can not be any of the others... z value of 1.00 |

ValeDeAcha |
Can someone tell me please in which page of the book do we find the "normal table"? |

ebayer |
in every stats book you will find such tables as appendixes. |

drb2234 |
So...anytime the question asks "x>20" - just as an example - you would subtract the z-score from 1? |

cfaeater |
The Z-tables can be found in the appendices in the CFA book Ethical and Professional Standards and Quantitative Methods. |

johntan1979 |
Just flip the arrow... both sides are symmetrical, meaning for P(x>20) is the same as P(x<60) |

Huricane74 |
For P(x>20) with a std. dev. of negative 4, I was looking for a probability of 99.99% because it is not quite 100%. I am going to hate questions like this on the CFA exam. It sucks when you know the answer, and you still get it wrong. |