Question

A quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct. If a student guesses on each question, what is the mean and standard deviation of the number of correct answers

Answer 1

The mean and standard deviation of the number of correct answers is 3 and 1.55 respectively.

Explanation:

We are given that a quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct.

Let X = the number of correct answers

The above situation can be represented through binomial distribution;

`P(X = x) = \binom{n}{r}* p^(r)* (1-p)^(n-r); x = 0,1,2,3,......`

where, n = number of samples (trials) taken = 15 multiple choice questions

r = number of success

p = probability of success which in our question is probability of

one correct answer out of 5, i.e; p =
`(1)/(5)` = 0.2

So, X ~ Binom(n = 15, p = 0.2)

Now, the mean of the number of correct answers is given by;

Mean of X, E(X) =
`n * p`

=
`15 * 0.2` = 3

And the standard deviation of the number of correct answers is given by;

Standard deviation, S.D.(X) =
`√(n * p* (1-p))`

=
`√(15 * 0.2* (1-0.2))` = 1.55