Seeing is believing!
Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation.
Basic Question 7 of 11
The bolts produced by M and K Steel have lengths with a mean of 3 cm and a standard deviation of 0.3 cm. A box of 200 of these bolts is considered a random sample. What is the probability that the average lengths of the bolts in the box are shorter than 2.95 cm?
B. 0.62%
C. 2.36%
A. 1%
B. 0.62%
C. 2.36%
User Contributed Comments 15
| User | Comment |
|---|---|
| vincenthuang | my answer=.94% |
| minna | how did you calculate, vincent? |
| gambary | how are you supposed to know the probability without a z table on the exam?? |
| ehc0791 | depending on how many digits you take on 0.3/sqrt(200), if you take 4, it will be 0.0212 then you will get the final result of .9% |
| gkobylko | Remember that for normal distribuition the probabilities of values falling within a number of deviations are: 1 stdev = 68% 1.65 stdev = 90% 1.96 stdev = 95% 2.5 stdev = 99% the z-score for this question is 2.357, close to 2.5, so the answer will be close to (1-.99)/2=.5% Only one obvious answer, no need to know the whole z table, just the key values |
| DannyZhou | What is 0+ and 1-? |
| tschorsch | some very tiny amount>0 (i.e. like 0.000001217372) some very tiny amount<1 (i.e. like 0.999991231231) |
| UFCRP | gkobylko, are you replying to Gambary? How would you discern 0.62% from normal distribution to get the correct answer. My guess is, you would need a Z table, wouldn't you? I'm confused. |
| DonAnd | vincent i got the same answer as you using all decimal places. I guess it's best to see how much d.p. is given in the amswer |
| tankdan | should provided z-table for these problems |
| johntan1979 | Best thing is don't round the intermediate steps. 0.94% is the precise answer. |
| GouldenOne | How is this question any different than the college X an Y example? They use 2 different methods to solve this problem |
| sgossett86 | this is b*llsh*t. -.05/.02121 = 2.357 so what the hell are they getting a z of 2.5 for? |
| sgossett86 | wow i feel like a retard. confidence intervals.. tail is half of the remainder to one. .5 on the south tail on the 99% CI. 2.5 on the south on the 95%. .6>.5 so just north of the 2.68 or < 2.68. I took a two week break from studying and look where it got me... jeeze... I need to hammer again. No more girlfriend... |
| maryprz14 | LOVE LOVE LOVE LOVEEEEE ANALYST NOTES... |
Thanks again for your wonderful site ... it definitely made the difference.
Craig Baugh
Learning Outcome Statements
explain the central limit theorem and its importance for the distribution and standard error of the sample mean
CFA® 2025 Level I Curriculum, Volume 1, Module 7.