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 , 





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