CFA Practice Question

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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?

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+.

User Contributed Comments 8

User Comment
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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