- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 3. The Central Limit Theorem

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**CFA Practice Question**

A population is known to have a left-skewed distribution with a mean of 400 and a standard deviation of 25. If a sample size of 50 is drawn at random from the population, what is the probability that the sampling distribution of the mean x-bar will have a mean less than 350?

A. P = 0.2106

B. P = 0.4798

C. P = 0.0000

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**User Contributed Comments**
8

User |
Comment |
---|---|

tenny45 |
can someone explain this? |

danlan |
Z=(350-400)/(25/sqrt(50))< -14, so the p is almost 0 |

julamo |
The way I do it: Around 97% of the observations lie above or below 2 standard deviations from the mean. In other words, in the population 97% of the observations will lie above 400-(2*25)=350. That leaves 3% below 350... A sample of 50 is 12.5% of the whole population so it's impossible to have a mean at 350 |

akanimo |
julamo your analysis would have been correct if you had used the correct value for standard deviation. You are using 25 (which is the population standard deviation) instead of using 25/sqrt(50) (as shown by danlan above) which is the sample standard deviation. If you do it this way you will find out that the standard deviation is 3.535 and 350 is about 14 standard deviations away! |

mchu |
central limit theorem... |

jackwez |
the more I look at these it just makes more sense to switch to reason vs memorizing all of this section's information... |

GBolt93 |
Yeah, I'd suggest understanding basic concepts and then using reason. |

bruno5104 |
So, I don't know if I got right but.. left skewed means that mean < median < mode.. it turns out that p < 350 gonna be almost 0 |