Re: Number of AA hands in one session -- help me figure this.
The standard deviation of the number of AA you will be dealt is equal to sqrt(1/221*220/221*240) which is a little above 1. This would then give you a result a of about 4.2.
However the 3 S.D. estimate is not very accurate in this case since this is a binomial random variable with mean near 1 and a number of trials much higher than that. A few further computations gives you P(5 AA or more)=.005027. P(4 AA exactly)=.0193789, so P(4 AA or more) is above .02. So we se the 3 S.D. estimate isn't extremely accurate in this case.
On a side note if the number of hands was say 2000 and you used the 3 S.D. estimate these would be the results.
mean +3S.D. is 18.05.
P(17 or more AA)=.0114823
P(18 or more AA)=.0055057
P(19 or more AA)=.0025129
So we see the higher N is the better of an estimate the 3 S.D. figure becomes.
|