Expectation of binomial distribution

Question

Given that $X\sim B(20,0.14)$ calculate $P(X\leq E(x))$.

My attempt,

I found that $E(X)=2.8$. How should I proceed?

Answer 1

You have correctly identified that $E\left[X\right] = np = 2.8$.
You are now interested in $P\left(X \leq 2.8\right)$, but since the Binomial distribution is supported for integer values only, we need only to consider the fact that: $$P\left(X \leq 2.8\right) = P(X\leq 2) = P(X=0) + P(X=1) + P(X=2)$$

Answer 2

This a hint, X takes integer values only, so $ X \leq 2.8 <==> X=0 $ or $ X=1 $ or $ X=2 $, so all you have to to do is to calculate $P(X=0)+P(X=1)+P(X=2)$