We believe that 90% of the population of all calculus i students consider calculus an exciting subject. suppose we randomly and independently selected 21 students from the population. if the true percentage is really 90%, find the probability of observing 20 or more of the students who consider calculus to be an exciting subject in our sample of 21.
Accepted Solution
A:
This is a binomial distribution problem. The formula to find the required probability is:
p(X) = [ n! / ((n - X)! · X!) ] · (p)ˣ · (q)ⁿ⁻ˣ
where: X = number of what you are trying to find the probability for = 20 or 21; n = number of events randomly selected = 21; p = probabiity of sucess = 0.9 (90%); q = probability of failure = 0.1 (10%);
We need to find the probability of two events: finding 20 students and finding 21 students. Therefore P(X) = P(X = 20) + P(X = 21).