- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 7. Estimation and Inference
- Subject 2. The Central Limit Theorem and Inference

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**CFA Practice Question**

The trees at CW Farms have heights that are normally distributed with a mean of 24 inches and a standard deviation of 2 inches. For a shipment of 25 trees (considered a random sample), what is the probability the average height for the shipment is less than 22 inches?

B. 0+

C. 15.87%

A. 0.1%

B. 0+

C. 15.87%

Correct Answer: B

The sampling distribution, the distribution of x-bars, for n = 25 has mean = 24 and standard deviation = 2/5 = 0.4. The z-score for 22 is (22 - 24)/0.4 = -5. The table value for -5, P(x-bar < 22), is out of the table. P(x-bar < 22) = 0+. So, the probability the 25-tree shipment has an average height of less than 22" is 0+.

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**User Contributed Comments**
8

User |
Comment |
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chenyx |
The standard error of the mean equal population standard deviation(2) divide by squear root of sample size(25).i.e.standard error=0.4. Under the sampling distribution(distribution of sampling means),the mean equal to the population mean(24), So: z-value=(22-24)/0.4=-5, it means that the probabiliti the 25-trees shipment has an average height of less than 22 is nearly 0. |

chenyx |
In contrast, the probabilities one tree has height of less than 22 is 15.87%.because the z-value=(22-24)/2=-1. |

NikolaZ |
How would you know whether this is a question that is a sampling distribution or just a sample (i.e. whether you would use the standard deviation when trying to find the z-score OR use the standard error?) ?? |

sgossett86 |
My guess is that they're specifically referring to a sample taken from a population for which they have established perameters. THey're not asking you to obtain statistics on the population. The population data is known. |

Yrazzaq88 |
Finally got this right... |

kaichan91 |
If I'm reading this correctly, you use standard error for when you are testing a sample *statistic* as opposed to sample observations. Correct me if I'm wrong... |

maryprz14 |
kaichan91; to answer your question I just copy and paste from the notes; "the STANDARD ERROR of a statistic is the STANDARD DEVIATION of the sampling distribution of that statistic." analyst notes has done an amazing job to explain this. when you take a sample from the population you should calculate the Standard error of the sample and use that as your Standard Deviation (for the sample). I hope I did not confuse you. |

maryprz14 |
and remember statistic vs parameter. |