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The standard deviation of the sampling distribution of the sample means is 20.8
What is Sample mean?
A sample is just a small part of a whole. For example, if you work for a polling company and want to know how much people pay for food a year, you aren’t going to want to poll over 300 million people. Instead, you take a fraction of that 300 million (perhaps a thousand people); that fraction is called a sample. The mean is another word for “average.” So in this example, the sample mean would be the average amount those thousand people pay for food a year.
The sample mean is useful because it allows you to estimate what the whole population is doing, without surveying everyone. Let’s say your sample mean for the food example was $2400 per year. The odds are, you would get a very similar figure if you surveyed all 300 million people. So the sample mean is a way of saving a lot of time and money.
Given that,
mean = = 20.8
standard deviation = σ = 4.2
n=89
So, The sampling distribution of the sample means is:
=
=20.8
Hence,
The standard deviation of the sampling distribution of the sample means is 20.8
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