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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... |
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Learning Outcome Statements
explain the central limit theorem and its importance for the distribution and standard error of the sample mean
CFA® 2024 Level I Curriculum, Volume 1, Module 7.