A random variable X follows the binomial distribution and X B(n, 0.3) . If the mean of X is three times as large as the standard deviation of X , then n=

Step-by-step solution

Given, p=0.3, q=1-p=0.7 Also, Mean ( )=3 Standard deviation ( ) . =3( ) ...(i) aligned & Now, =n p=0.3 n & and = n p q = n(0 3)(0 7) = 0.21 n & From Eq. (i), (0.3) n=3 (0.21) n aligned array ll & (0.1) n= (0.21) n & ( n 10 )^2= ( 21 n 100 ) & n^2-21 n=0 n(n-21)=0 & n=0,21 array But n 0 Thus, n=21 .