SOLUTION: A population has a mean 88 and a standard deviation 18. Find the mean and standard deviation of a sampling distribution of sample means with sample size n 81.

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Question 1201486: A population has a mean 88 and a standard deviation 18. Find the mean and standard deviation of a sampling distribution of sample means with sample size n 81.
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer:
mean = 88
standard deviation = 2


Explanation:

xbar = sample mean
The xbar distribution is the distribution of various sample means from the same population.
If we were to repeatedly take random samples of n = 81, compute the sample mean, then this is one of the many xbar values.

The center of the xbar distribution is mu = 88 which is where all of the xbar values should cluster around.

The standard deviation of the xbar distribution is
sigma/sqrt(n)=18/sqrt(81)
=18/9
=2
where sigma is the population standard deviation.
This tells us how spread out the distribution is.