The sum and product of the mean and variance of a binomial distribution are 82 . 5 and 1350 respectively. They the number of trials in the binomial distribution is

Step-by-step solution

Given, sum of mean and variance is 82 . 5 Product of roots is 1350 Now, Mean and variance are the roots of x 2 - sum of roots x + product of roots = 0 ⇒ x 2 - 82 . 5 x + 1350 = 0 ⇒ x = 60   or   22 . 5 So, mean = n p = 60 and variance = n p q = 22 . 5 ⇒   q = 22 . 5 60 = 3 8 So, p = 5 8 and n = 60 5 8 = 96