SOLUTION: Consider a population with a mean of 25 and a standard deviation of 4. A sample of 100 people is taken from the above population. What is the standard deviation of the 100-perso

Algebra.Com
Question 1198132: Consider a population with a mean of 25 and a standard deviation of 4.
A sample of 100 people is taken from the above population.
What is the standard deviation of the 100-person sampling distribution

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 0.40


Explanation:

n = 100 = sample size
sigma = 4 = standard deviation
SE = standard error
SE = standard deviation of the xbar distribution
SE = sigma/sqrt(n)
SE = 4/sqrt(100)
SE = 4/10
SE = 0.40

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.

The standard error tells us how spread out the xbar distribution would be. The larger the SE value, the more spread out the data values are.

RELATED QUESTIONS

Consider a population with a mean of 25 and a standard deviation of 4. A sample of 100... (answered by ewatrrr)
Consider an infinite population with a mean of 160 and a standard deviation of 25. A... (answered by stanbon)
consider an infinite population with a mean of 160 and standard deviation of 25,a random... (answered by stanbon)
Given a population with a mean of 170 and a standard deviation of 12. With a sample of 50 (answered by stanbon)
Consider a large population with a mean of 100 and a standard deviation of 21. A random... (answered by robertb)
Consider a normal population with a mean of 50 and standard deviation of 2. A random... (answered by Boreal)
Suppose a random sample of 50 values is taken from a normal population with standard... (answered by ewatrrr,stanbon)
A sample of 64 was taken from a population, with the mean of the sample being 119 and the (answered by Boreal,rothauserc)
A normally distributed population with 100 elements has a mean of 60 and a standard... (answered by Edwin McCravy)