Let a random variable X have a Binomial distribution with mean 8 and variance 4 . If P(X 2)= K 2¹⁶ , then K is

Step-by-step solution

Let X B ( n , p ) According to the given conditions, Mean =n p=8 and variance =n p q=4 p = q = 1 2 and n =16P(X 2)= K 2¹⁶ P ( X =0)+ P ( X =1)+ P ( X =2)= K 2¹⁶ aligned ¹⁶ C ₀ ( 1 2 )^0 ( 1 2 )¹⁶+ ¹⁶ C ₁ ( 1 2 )^1 & ( 1 2 )¹⁵ & + ¹⁶ C ₂ ( 1 2 )^2 ( 1 2 )¹⁴= K 2¹⁶ aligned array ll & 1+16+120 2¹⁶ = K 2¹⁶ & K=137 array