Answer :

Let n and p be the parameters of the required binomial distribution. So,


1 - p = q






Also,







625q = 150[(1+q)2]


25q = 6[(1+q)2]


6 + 6q2 + 12q – 25q = 0


6q2 – 13q + 6 = 0


6q2 – 9q - 4q + 6 = 0


3q(2q - 3) - 2(2q - 3) = 0


(2q - 3)(3q - 2) = 0


(2q - 3) = 0 or (3q - 2) = 0



As, q≤1



Now, p = 1 - q







n = 15


The required binomial distribution is given by,



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