A certain class is given a multiple choice exam of 20 questions with each questi

Question

A certain class is given a multiple choice exam of 20 questions with each question having four possible answers. A student does not study and randomly guesses on all of the questions. Let X = the # of questions the student gets correct. What is the probability that a student answers at most 5 questions correctly?. What is the probability that the student answer exactly 5 questions correctly? What is the number of questions a student guessing at random will get correct? What is the standard deviation of the number of questions a student guessing at random will get correct?

Explanation / Answer

a. P(X<=5 ) = 20C0(.25^0)(.75^4)+..20C4(.25^4)(.75^0) = 0.415

b. P(X=5) = 20C4(.25^4)(.75^0) = .202

c. This is the mean number = np = 20*1/4 = 5

d. This is the standard devition given by sqrt(npq) = sqrt(5*.75) = 1.936

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