- 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**

An analyst who manages an equity portfolio forecasts a portfolio return of 10% and estimates a standard deviation of annual return of 18%. What is the probability that the portfolio return will be between 10% and 20%?

A. 18.7%

B. 19.67%

C. 21.2%

**Explanation:**The probability is 21.2% that the portfolio return will be between 10% and 20%:

Z = (X - X-bar)/σ

X = 10%: Z = (10% - 10%) /18% = 0.

X = 20%: Z = (20% - 10%) /18% = 0556.

A Z-value of 0 gives us 0.5 on the table. A Z-value of 0.56 gives us 0.7123 on the table.

The solution is 0.7123 - 0.50 = 0.2123 = 21.23%.

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**User Contributed Comments**
12

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

ramtor |
do we have to memorize the z table. |

smiley25 |
If I remember correctly from december's paper last year, we were not given any tables. One can assume you must know 68%=1sd; 90%=1.645sd; 95%=1.96sd; 99%=2.58sd from mean. |

EtnicPlaymaker |
P( -1 < z < 1 ) = 68% => P( z < 1 ) = 68% + 32%/2 = 84% P(a < z < b) = P z < b) - P (z < a) = = P (z < 0,556) - 0,5 < 84% - 50% = 34% => Without z-table it's impossible to answer correctly. |

achu |
If they don't give us a table, just send a protest. It is NOT reasonable to expect students to memorize the z (or t) tables. I'm sure they won't do that... |

baddabing |
They will not provide any tables on the exam UNLESS the question relates specifically to it. If this is the case they will have a part of the table only (and directly below the question. |

visiblebob |
I would also learn that 85% = 1.44. |

JonClark |
I understand the statistics and the z table. But why is Xbar 10%? I don't understand how you get that from "an analyst forecast". Can anyone explain? |

Jurrens |
I would remember the values based on Z and not on the %'s... otherwise, you'll find yourself getting confused about one and two tailed tests. |

Jurrens |
and ? = - ni their solution above. I was confused about that for a minute. |

ksnider |
STUPID QUESTION, how do we figure this out without the use of a z table?? |

nmech1984 |
Z Table Formula to calculate approx Z (my invention) Approx Z = 0.14*e^(0.28x) where x->0 to 1 You can also remember like this: Approx Z = 0.14*e^(0.14*20*x) For example if you put x=0.95 then Approx Z = 2.0014, not the samebut close to the real Z. |

nmech1984 |
Approx Z = 0.14*e^(2.8x) |