Question

HW4.5. Multiple-choice Test A multiple-choice test has 43 questions. Each question has 4 choices. If you guess at random on all the questions and each guess is independent from one another, what are the expected value and standard deviation of the number of correct answers on your test? 1. What is the expected value of the number of correct answers on your test? (a) 10.75 (b) 21.5 (c) 8.75 (d) 11.75 2. What is standard deviation of the number of correct answers on your test? (a) 2.84 (b) 5.68 (c) 32.25 (d) 8.06

Answer 1

X=guessing a answer

n=43

p(success)=$\frac{1}{4}$=0.25

q(failure)=1-p=1-0.25=0.75

X~binom(43,0.25)

1.

E(X)=np

E(X)=43*0.25

E(X)=10.75

hence, option(A) 10.75 is correct.

2.

Var(X)=npq=43*0.25*0.75

Var(X)=8.0625

standard deviation=$\sqrt{Var(X)}$=$\sqrt{8.0625}$

standard deviation=2.84

hence,option(A) 2.84 is correct.

please rate my answer and comment for doubts.

Answer 2

The answer to 1 is A.