### CFA Practice Question

There are 985 practice questions for this topic.

### CFA Practice Question

Suppose that the penalty for withdrawing funds early from a certain account follows a uniform distribution on the interval from (5%,12%). What is the probability that the penalty is between 6% and 9%?

A. 0.143
B. 0.429
C. 0.882

The probability is P(6 < X < 9) = F(9) - F(6) = (9-5)/7 - (6-5)/7 = 0.429.

### User Contributed Comments18

User Comment
mtcfa Huh??? Obviously I'm screwed on this section.
dave79 Acutally, it's not that difficult:
here is answer -
1) Find a and b in this problem 5=a and 12=b
2) now need to find probablity between 6% and 9% which lies betn distribution a and b
3) P(6<x<9) is equal to cummulative prob of 9 - cumm prob of 6 = F(x=9) - F(x=6)
4) F(x) = x-a/b-a
5) F(9) = 9-5/12-5 and F(6)= 6-5/12-5
6) = 4/7 - 1/7 = 3/7 =0.429
Bibhu Good explanation dave.
bahodir Wait a minute... (5, 12) means 6, 7, 8, 9, 10, 11, doesn't it? The question should have written [5, 12] if they included 5 and 12 in the solution.
bahodir Oh, I instead of 6, 7, 8, 9, 10, 11 I mean the range from 5 to 12 excluding these two numbers.
Christian07 Why doing it that difficult? Total range => 12-5= 7, Selected Range => 9-6=3, therefore 3/7=0.429
bobert bahodir, you are correct that the numbers are not inclusive. BUT, because it is a uniform distribution, we are assuming it is continuous. Due to this fact, we know that the probability for a continuous random variable p(x) = 0 because there are an infinite number of possibilities. So just for the sake of correctness, the actual list of 6,7,8,9,10,11 is not important because each individual variable would then be p(6)=0, p(7)=0, and so on. What is important is the range of values between 5 and 12 and the formula to find the percentage of values within the parameters. This problem is asking for a CUMULATIVE probability within the parameter in reference to the range.
rt2007 this is the formulae - (X2-X1)/(b-a)
madhi Remember that we are trying here to compute an area of a rectangle.

Hight of Rectangle = 1/(b-a)

Required interval = 9%-6% = 3%

Hence, the required probability equals the partial area = 3%/(b-a) = 3%/7% = 0.429
Meka76 Thanks guys, this really helped.
CFAonTheBrain i'm not sure what im doing is right but i did this--- 5 - 12 = 7 and then 6 - 9 = 3 so 1/7 + 1/7 + 1/7 = .429 or .4285
jansen1979 Just draw a box with a minimum of 5 and a maximum of 12 and see which part you need to cover, will come clear this way.
boddunah good question
bp019j Thanks Christian07
cfaeater Great answer Christian07 - no nonsense explanation.
sgossett86 Yeah, I did what Christian did intuitively. I'll memorize and apply the formula as needed, but I'm tired and this was an intuitive way.
praj24 MAN LIKE CHRISTIAN07
cfastudypl Thanks Christian07 for the astute solution.