Question

In a binomial distribution, `n=8` and `p = .3`. What is the probability `x<=2`?

Answer 1

I got roughly `0.55`

Explanation:

The general form of a binomial probability is:

`sum_(k=0)^(n)C_(n,k)(p)^k(~p)^(n-k)=1`

With `n=8, p=.3, ~p=.7`, we are looking at `k=0,1,2`:

`C_(8,0)(.3)^0(.7)^8+C_(8,1)(.3)^1(.7)^7+C_(8,2)(.3)^2(.7)^6~~0.55177~~0.55`