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Binomial Distribution: Summary Notes Conditions for the binomial distribution: Fixed number of trials, n Only two possible outcomes, success or failure Probability of success does not change, p Notation for binomial distribution: X B n, p Ways of calculating binomial probabilities: Binomial cumulative tables give P X r Binomial formula gives P X r . Formula is P X r n Cr p r 1 p nr Mean and variance of a binomial distribution: np 2 np 1 p So, of course the standard deviation is given by np 1 p