CFA Practice Question

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CFA Practice Question

The lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximately ______.

A. 0.20
B. 0.5793
C. 0.4207
Correct Answer: C

The z-score corresponding to 520 is (520 - 516)/20 = 0.2. The area to the right is 1 - 0.5793 = 0.4207, which corresponds to the proportion with lifetimes exceeding 520.

User Contributed Comments 17

User Comment
Will1868 z-tables on exam?
nchilds no... very unlikely. As for what I saw, CFA Institute will most likely give you the confidence interval (i.e. 95%) and you will have to know the Z score (i.e. 1.96). Also, they tend to give you an uncommon interval, that they don't expect you to know (like 2.0), but since you know that 1.96 = 95 % you should be able to get the answer via solving the problem using 1.96 and finding the best fitting answer.
BonnieG than how would you come up with .5793 w/out a z-table?
mtcfa The z-table I'm looking at shows a proportion with a z-score of .2 to equal .0793. Where did this .5793 come from?
grantw you need to add 0.5.
gizi The z score for .2 is .5793 not .0793. No need to add .5!
tanyak The Z score is always the area BELOW the mean..520 is clearly above the we need to 1-0.5793
bobert gizi, the z-score for .2 is .0793. It is .5793 on the cumulative z table
Nicholas folks, with the choices given, think graphically and this one is a lay-up
StanleyMo as we got Z=>0.2, the probability is defintely less than 0.5, as the for Z<0 will take 0.5, and 0<z<0.2 will take some portion as well, so getting 0.4xxx is reasonable. This kins of Q did not need the table of Z
chamad Good point stanleyMO
Beret Did the exam once and there was never any z-table
johntan1979 Don't be ridiculous. I did the exam too, and the table is provided next to the question where it is needed (not a separate piece of paper).
johntan1979 I meant the information needed from the table, not the actual table. Still need to know the calculations and the concept to make use of the data provided. CFA won't leave you guessing the nearest answer.
sgossett86 To be honest if you know the critical values and you're left with choices like those you can sensibly derive the answer through ruling out unrealistic ones. It was .2 standard deviations away from mean. You know that it's in the first confidence interval of 68%, only .2 so .5 of the 68% is above mean, so 2/5ths of 34% puts you at 63% so you know that if it's linear 36% is above the SD, not 20. I'm going off in a tangent here but what i'm saying is reason can get you there.
PSVC Z-Table value for 0.2 = 0.5793.
Therefore as 520 is above the mean the correct answer would be 1-0.5793. In this case,C.
Kevdharr Just think about it this way: Your Z-score is 0.2. If you memorize the following confidence intervals and Z-scores, you should get this right by process of elimination. Even without a table, we know that:
-50% of all observations fall within 0.67 standard deviations of the mean
-68% of all observations fall within 1 standard deviation of the mean
-95% of all observations fall within 1.96 standard deviations of the mean.
99% of all observations fall within 2.58 standard deviations of the mean.

Therefore, if the Z-score is 0.2, that means that it is less than 0.67 (which is the lowest z-score we have to memorize). If you know that with a z-score of 0.67, the confidence interval (i.e., probability) is 50%, then with a LOWER z-score (i,e., 0.2), you have to have a confidence interval/probability of LESS than 50%. The only option here is C (0.4207) if you exclude choice A (0.2) which you know is the Z-score itself. NOT the confidence interval.
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