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Basic Question 10 of 11
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%
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. |
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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® 2025 Level I Curriculum, Volume 1, Module 7.