### CFA Practice Question

Past experience of a large manufacturing firm with administering a test to recent college graduates who had applied for a job revealed that the mean test score was 500 and the standard deviation was 50. The distribution of the test scores was normal. Based on this experience, management is considering placing a person whose scores are in the upper 6 percent of the distribution directly into a responsible position. What is the lowest score a college graduate must earn to qualify for a responsible position?
A. 625
B. 460
C. 578
Explanation: Find the z value representing 44% of the area under the curve. From the z tables, z = 1.55. Use z = (x-u)/sigma. 1.55 = (x-500)/50. x = 577.5

User Comment
sireklove Will the z tables be given to us in the exam?
ticomico I don't think so.
Alastair you know that z<1.64, so only C fits.
lwang014 z<1.64,I agree!
Rguerra The z tables will not be provided. This is the kind of question you have to do by aproximation.
julamo You don't even need to bother with the z tables... You know that 98% of observations are located within 2 standard deviations from the mean. On the upside it gives 600. the question asks for the upper 6%, considering all the options, C has to be the right answer.
ontrack Julamo has got the trick! If 95% of score is within mean+2sigma=50+2*50=600 then the top6% score will begin slightly less than 600 -->578
steved333 z is approximately 1.5 since 1.645 is 90%, and we're talking about 88%. 1.5*50=75 added to 500=575, which is dangerously close to 578...
vikram59 why are we talking 88%???
grezavi No 88% if anything it is a one-tailed test with the upper % of the scores read "julamo" and "ontrack" for this one above
bodo agree with ontrack, using z=1.58 for 95% you get from teh equation 579 very close to the correct answer. on the exam z tables are given but we ought to know z for 99%, 95% and 90%
bhaynes RGuerra- I can tell you from experience of taking this already that they absolutely give you the table you need for this. In fact, you get an entire booklet of z-tables, t-tables, F-test, etc. I was be unreasonable and proposterous if they expected you to memorize the tables.
Andy552 I understand how you can get the question by guessing based on 2x standard deviations. But why do they look up 44% in the Z tables?
Andy552 nvm, we're only looking at one side of the curve!
moneyguy The tables will not be provided. The tables will be provided. I'll listen to those who've taken the exam previously. We get the tables, for gosh sakes!!
divyapeddi same question as andy552. Why do we look for 44% in z tables?
rabihCH 44%=50%-6%
88%=100%-12%
Lambo83 This has to be incorrect. The max score is 695 so the answer is 653.3.

If the standard deviation is 50 and the mean is 500, and the maximum standard deviations away from the mean in a normal distribution is 3.9. Then

max score = 500 + (50 x 3.9) = 695.

Then to be in the top 6%: 695 x (1 - 0.06) = 653.3
mlaique listen to julamo and ontrack