Binomials and random variables

Question

We believe that 95% of the population of all Calculus I students consider calculus an exciting subject. Suppose we randomly and independently selected 20 students from the population. If the true percentage is really 95%, find the probability of observing 19 or more of the students who consider calculus to be an exciting subject in our sample of 20.

Answer 1

SInce you just have to add P(X = 19) + P(X = 20), you can either provide the closed-form solution for P(X = 19, n = 20, p = .95) + P(X=20, n = 20, p = .95) or use a package. Using a package, you would calculate 1- P(X <= 18, n = 20, p = .95)

The closed form is C(20,1) * .95^19 * .05^1 + .95^20 = 20 * * .05 + =

+ =

Using Excel, the solution is 1 - binom.dist(18, 20, .95, 1) =