Let X be a binomial random variable with EX 7 and VarX 21

Let X be a binomial random variable with
E(X) = 7, and Var(X) = 2.1.
(a) Compute P(X = 8).
(b) Find P(X > 11).

Solution

Let X be a binomial random variable with
E(X) = 7, and Var(X) = 2.1.

E(X) = np= 7, and Var(X) = npq=2.1.

Therefore q =2.1/7=0.3

p=1-q=0.7

n=10

(a) Compute P(X = 8).

P(X=x) = (_nC_x) p^x (1-p)^n-x   

P(X=8) = (₁₀C₈) 0.7⁸ (1-0.7)^10-8   

P(X = 8) = 0.2334

(b) Find P(X > 11) = 0.0   ( since X > n=10)