For a Binomial distribution with mean 6 and standard deviation 2 , what is the value of P(X=0) ?

Step-by-step solution

Let n be the number of trials and p be the probability of success. Mean = np = 6 Standard deviation = npq = 2 Variance = npq = 2 Dividing the variance by the mean: npq np = 2 6 q = 1 3 Since p + q = 1 , we get p = 2 3 . Substituting p into the mean equation: n ( 2 3 ) = 6 n = 9 The probability of X = 0 is given by: P(X=0) = ^ n C₀ p^0 q^n P(X=0) = ⁹C₀ ( 2 3 )^0 ( 1 3 )^9 = ( 1 3 )^9 Answer: ( 1 3 )^9