If x is a binomial random variable, compute P(x) for each of the following cases

Question

P(x<or=3), n=8, p=0.4

P(x)=?

P(x>3), n=8, p=0.3

P(x)=?

P(x<1), n=8, p=0.3

P(x)=?

P(x>or=7), n=9, p=0.3

P(x)=?

Answer 1

X ~ Binomial (n,p) where n is the sample size and p is the success probability.

Each question will require a binomial probability distribution formula. You may use the binomial distribution probability calculator for each one.

P(X = x) = C(n,x)*p^x*(1 - p)^{n - x} = n!/[x!(n-x)!]*p^x*(1 - p)^{n - x}

1.) P(x ≤ 3), n=8, p=0.4

P(x) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.5941

2.) P(x > 3), n=8, p=0.3

P(x) = 1 - P(X ≤ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)] = 1 - 0.8059 = 0.1941

3.) P(x < 1), n=8, p=0.3

P(x) = P(X = 0) = 0.0576

4.) P(x ≥ 7), n=9, p=0.3

P(x) = P(X = 7) + P(X = 8) + P(X = 9) = 0.0043