Question 1198178: Consider a population with a mean of 25 and a standard deviation of 4.
What is the standard deviation of the 100100-person distribution?
Choose one of the following:
A) 4
B) .04
C) .40
D) unable to determine from the information given
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: C) 0.40
Explanation:
It seems like there's a typo with the value 100100
I'll show what happens when we use this as the sample size.
n = 100100
sigma = 4 = standard deviation
SE = standard error
SE = standard deviation of the xbar distribution
SE = sigma/sqrt(n)
SE = 4/sqrt(100100)
SE = 0.01264279082482
SE = 0.01
This answer choice isn't listed.
Now I'll use n = 100 since it appears you meant to say this, but somehow the value was typed twice (or copy/pasted in a strange format). Please be careful and review the question fully before posting.
So,
SE = sigma/sqrt(n)
SE = 4/sqrt(100)
SE = 4/10
SE = 0.40
This is listed as choice C, so it's likely you meant to say n = 100.
The xbar distribution refers to the distribution of sample means (xbar). In this case, we sample 100 people at random, compute the xbar of said sample, and that value is tossed into the distribution. Do this enough times and you'll get a dot plot to help form some kind of distribution curve.
As n gets larger, the xbar distribution starts to resemble the normal distribution, aka gaussian distribution. See the central limit theorem in statistics.
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