SOLUTION: Suppose the mean GPA of students is 3.7 and the standard deviation is 0.9. It is well known that this distribution is left-skewed.
If you take a random sample of 64 students, wh
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Question 875395: Suppose the mean GPA of students is 3.7 and the standard deviation is 0.9. It is well known that this distribution is left-skewed.
If you take a random sample of 64 students, what is the mean and standard deviation of the distribution of sample means of these GPA scores?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the mean gpa of students is 3.7 and the standard deviation is .9
the distribution is left skewed.
you take a random sample of 64 students.
since you have a relatively large sample size (> 30), the distribution of the sample means is assumed to be normal.
the standard error of the distribution of the sample means is equal to .9/sqrt(64) which is equal to .9/8 which is equal to .1125
the mean of the distribution of sample means is assumed to be the same as the mean of the population which is equal to 3.7.
the standard deviation of the distribution of sample means is equal to the standard error which is equal to .1125.
here's an online demo that shows you that the distribution of sample means is very close to normal if the sample size is large enough regardless of the shape of the population distribution.
that's called the central limit theorem.
http://www.stat.tamu.edu/~west/ph/sampledist.html
i think you need to have java enabled in order to see it.
here's a picture of one demo i ran in case you can't run it yourself.
the green distribution is the distribution of sample means.
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