SOLUTION: A die is rolled 480 times. Find the mean, variance, and standard deviation of the number of 3's that will be rolled. Is it unusual to roll three 100 times?

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Question 1028526: A die is rolled 480 times. Find the mean, variance, and
standard deviation of the number of 3's that will be
rolled. Is it unusual to roll three 100 times?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A die is rolled 480 times.  Find the mean, variance, and standard 
deviation of the number of 3's that will be rolled.  Is it unusual 
to roll three 100 times? 

This is a binomial probability, with n=480, p=1%2F6

mean+=+mu+=+n%2Ap=+480%2Aexpr%281%2F6%29=80
variance+=+sigma%5E2+=+n%2Ap%2A%281-p%29+=+480%2Aexpr%281%2F6%29%281-1%2F6%29=66%262%2F3
matrix%281%2C2%2Cstandard%2Cdeviation%29=sigma=sqrt%28variance%29=sqrt%2866%262%2F3%29=8.165

An event is unusual if the probability of occurring is less than
5% or 0.05, which will be an event whose measure is more than 1.645
standard deviations either above or below the mean.

100 is 20 more than the mean. 1.645 times the standard deviation
is 13.431.  So indeed '20 more than the mean' is more than '13.431
more than the mean', so it is unusual to roll 100 3's out of 480 times.

Edwin