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

Step-by-step solution

Let X B ( n , p ) According to the given conditions, mean = np =8 and variance = npq =4 p = q = 1 2 and n =16 P ( X 2)= K 2¹⁶ P ( X =0)+ P ( X =1)+ P ( X =2)= K 2¹⁶ 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 1+16+120 2¹⁶ = K 2¹⁶ K =137