### CFA Practice Question

There are 434 practice questions for this study session.

### 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%.

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)