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?
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
|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.|