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

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

Step-by-step 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;

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 = = 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) =

                                    = = 3

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

       Standard deviation, S.D.(X) =

                                                     =  = 1.55

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