Question

4. Final exam has 20 multiple choices questions. 10 questions have 5 choices and 10 questions have 4 choices. In each question, only one of the choices is the correct answer. Now assume that you just randomly pick the choices. If X is the number of questions which you choose the right answer, what is the standard deviation of X?

Answer 1

1.844

Explanation:

Given that final exam has 20 multiple choices questions. 10 questions have 5 choices and 10 questions have 4 choices.

So we divide the questions into two groups I and II.

The no of correct answers in I is called U.

U is binomial with n =10 and p = 0.2

Similarly II group, V the no of correct answers would be binomial

with n =10 and p = 0.25

Our random variable X= U+V

Obviously U and V are independent.

We have var (U) = npq = 1.6

Var (V) = npq = 1.875

Var(X) = Var(U+V)

= Var(U)+Var(V) since U and V are independent

= 3.4

STd dev (X) =
`√(3.4) \\=1.844`