If the mean and variance of a binomial distribution is 24 and 8, find the value of n.

12

Mean = np

and Variance = npq

Where, p = probability of success and q = probability of failure

np = 24    -----(1)

npq = 8

 np (1 - p ) = 8           ( q = 1 - p )

By using equation 1 ,

24 ( 1 - p ) = 8

p = 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)

Now,

np = 8

n × \(\frac{2}{3}\) = 8

n = 12

The correct answer is Option (1) → 12