Question 1206822: Random samples of size 53 are drawn from a population with mean 104.3 and standard deviation 21.8. Find the mean and the standard deviation of the sample mean. Round to four decimal places.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! given the population mean and the population standard deviation, .....
the mean of the distribution of sample means is equal to the population mean.
the standard deviation of the distribution of sample means is equal to the population standard deviation divided by the square root of the sample size.
in this problem,...
mean of distribution of sample means = 104.3.
standard deviation of distribution of sample means = 21.8 / sqrt(53) = 2.9945 rounded to 4 decimal places.
note that the standard deviation of sample means is also called standard error.
here is a reference on the central limit theorem which is the theory behind the meaning of the distribution of sample means.
https://www.scribbr.com/statistics/central-limit-theorem/#:~:text=The%20central%20limit%20theorem%20states,population%20isn't%20normally%20distributed.
there are many references on the web for the central limit theorem.
if this one doesn't satisfy you, select another, and another, until you find one that you can understand clearly.
this one, i found to be pretty good and fairly easily explained.
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