Download A quiz consists of five multiple-choice questions with

A quiz consists of five multiple-choice questions with five choices for each question (A, B, C, D, & E).
A. If a student randomly guesses on each question, what is the probability that he/she passes if at least
three correct answers are needed to pass? Please round the answer to the thousandths place.
B. What is the mean of the number of questions answered correctly for this quiz?
C. What is the standard deviation for the number of questions answered correctly for this quiz?
A: It is a binominal problem.
Guess from (A, B, C, D, & E) , then p(success) = 1/5, 1- p(success) = 4/5
Let k is number of corrected answered. The problem is:
P(k>=3)=?
P(k>=3) =p(k=3) +P(k=4) +(k=5) By binomial distribution
= 3C5*p3(1-p)5-3+4C5*p4(1-p)5-4+5C5*p5(1-p)5-5 (3C5 means choose 3 from 5)
= 0.05792
B: mean of the number of questions answered correctly
= E(k) (E means expectation)
= sumi(i*p(k=i)) = 1*p(k=1) + …+ 5*p(k=5)
= 1*1C5*p1(1-p)5-1+…+5*5C5*p5(1-p)5-5
=1
Another simple way is: E(k) =n*p = 5*(1/5) =1. n is number of questions
C: V(k) = n*p*(1-p) = 5*(1/5)*(4/5) = 4/5