Previous Problem Problem List Next Problem 1 point) Instead of studying for an u

Question

Previous Problem Problem List Next Problem 1 point) Instead of studying for an upcoming multiple-choice exam, a friend of yours decides to randomly guess at each answer and hope that enough answers end up being correct. You are going to try to convince your friend that this is a bad idea. You friends says the exam will have 10 questions. (a) If each question has four choices, your friend has a 25% chance of guessing the correct answer to any given question. Assuming your friend independently guesses each answer, what is the probability that he/she guesses correctly on 5 or more questions (and thus scores 50% or better)? (give the answer to four decimal places) (b) If each question has five choices, your friend now has only a 20% chance of guessing the correct answer to any given question. Assuming your friend independently guesses each answer, what is the probability that he/she guesses correctly on 5 or more questions (and thus scores 50% or better)? (give the answer to four decimal places)

Explanation / Answer

This is a case of binomial distribution where n is 10

a) p is given as 0.25

thus using Excel we get P(x>=5)=1-P(x<=4)=1-BINOM.DIST(4,10,0.25,TRUE) = 0.0781

b) p is given as 0.2

thus using Excel we get P(x>=5)=1-P(x<=4)=1-BINOM.DIST(4,10,0.2,TRUE) = 0.0328

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