- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 3. Standard Error of the Sample Mean

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**CFA Practice Question**

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%

Correct Answer: B

Because the sample size is large (n > 30) the distribution of the x-bars is approximately normal with mean 3 and standard deviation 0.3/sqrt(200) = 0.02. Now, the z-score for 2.95 is (2.95 - 3)/0.02 = -2.5. The table value for -2.5 is 0.0062. So, P(x-bar < 2.95) = 0.62%. The probability that the average length of the bolts in the box of 200 bolts is less than 2.95 cm is 0.62%.

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**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... |