The random variable X follows a binomial distribution B(12,0.2).?

Question

Find the smallest value of x such that P(X<= x)> 0.7
The answer is 3

mean is 12*0.2 =2.4 can u give the method

Answer 1

P(X=0) = 0.8^12 = 0.0687
P(X=1) = 12 x 0.2 x 0.8^11 = 0.2062
P(X=2) = 12C2 x 0.2^2 x 0.8^10 = 0.2835
P(X=3) = 12C3 x 0.2^3 x 0.8^9 = 0.2362

P(X<=2) = 0.0687 + 0.2062 + 0.2835 = 0.558

P(X<=3) = 0.0687 + 0.2062 + 0.2835 + 0.2362 = 0.795
Since a value of 2 is less than 0.7 and a value of 3 is greater it follows that x = 3

Answer 2

I think you've answered your own question :-)