Suppose I give the class a multiple choice exam with 20 ques

Suppose I give the class a multiple choice exam with 20 questions, each with five possible selections (A, B, C, D, E) for the answer. Suppose that the student was unable to find time to study for the exam and randomly guesses for each question. Find the probability that the student gets at least one question correct. Find the probability that the student gets 90% or better on the exam. How many questions would you expect the student to get correct? Obtain the standard deviation of the number of questions that the student gets correct.

Solution

No of questions = 20

Possible choices =5

Prob for selecting one right answer = 1/5 =0.20

Each question is independent of the other

and there are two outcomes.

Hence X = no of questions right is binomial (20, 0.20)

a) P(X>=1) = 0.9885

b) P(X>= 0.9(20))

= P(X>=18) <0.00001

c) E(X) = np = 20(0.2) = 4

d) Var(X) = npq = 3.2

std dev = 1.7889