16. find the probability that the number x of correct answer is at least 3. 18. find the probability that the number x of correct answer fewer than 3.

Question

assume that random guesses are made for five multiple-choice question on an ACT test, so that there are n=5 trials. each with probability of success (correct) given by p=0.20. use the binomial probability table to find the indicated probability for the number of correct answers.

                                                                     

Answer 1

Well, I don't have a binomial probability table (I use a calculator), but the set-up is like this:

 

P(X is at least 3) = P(X>=3) = P(X=3) + P(X=4) + P(X=5) = (5 c 3)(.2)³(.8)² + (5 c 4)(.2)⁴(.8) + .2⁵

 

P(X is fewer than 3) = P(X<3) = P(X=0) + P(X=1) + P(X=2) = .8⁵ + (5 c 1)(.2)(.8)⁴ + (5 c 2)(.2)²(.8)³

 

You may not need to know those bold calculations if you are using a table, but the set-up should match.

 

J.T.