- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 6. Confidence Intervals for the Population Mean

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**CFA Practice Question**

Crop researchers plant 100 plots with a new variety of corn. The average yield for these plots is x-bar = 130 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean μ and standard deviation σ = 10 bushels per acre. A 90% confidence interval for μ is ______.

Correct Answer: 130 ± 1.645

Here x-bar = 130, n = 100, σ = 10 and z = 1.645, so our interval is 130 ± 1.645.

Recall that a confidence interval for the mean μ of a normal distribution with standard deviation σ is x-bar ± zσ/n

^{1/2}.Here x-bar = 130, n = 100, σ = 10 and z = 1.645, so our interval is 130 ± 1.645.

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**User Contributed Comments**
9

User |
Comment |
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whiteknight |
how to find z value for a given confidence interval ? |

eb2568 |
It is recommended that you know the values for the 90, 95, and 99 by heart going into the exam for conveniences sake. but the 90% interval is 1.65 (or 1.645), 95% is 1.96 and 99 % is 2.58...i think those numbers are right, but check for yourself to make sure. that number then is simply multiplied by the sd/n1/2 which in this case is simply 1 |

Yurik74 |
also Z for 80% could be useful = 1.282 |

allodrfc |
I wouldn't recommend it - there's no point in trying to remember something when you can easily look up the data on the z table. I'm saving my brains ever smaller capacity to remember things for things that aren't written down. |

SKIA |
allodrfc: I don't think they give you z tables for the exam. So having them memorized is probably a smart idea! |

sgossett86 |
I thought that since they gave us the standard deviation of the population (10) that we wouldn't have to calculate standard error of the statistic distribution... Can anyone touch on this with a little more precision for me please? If not I'll look it up.. |

tomalot |
So is it 1.645 x 10 bushels, either side? |

tomalot |
Ahhhh..multiplied by 10 and then divided by 10 |

Sagarsan88 |
Why are we using a Z, isnt t a better indicator in this qstn? As the population variance is unkown? |