Question

A quiz consists of 40 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? Round to the nearest thousandth.

Answer 1

8 and 2.529

Explanation:

The computation of the mean and the standard deviation is shown below:

Given that

Total number of questions is n = 40

The Probability of correct answer is p =
`(1)/(5)`

So, the probability of the wrong answer is q =
`1 - \frac {1}{5}` =
`(4)/(5)`

Moreover, this is the binomial distribution

Based on the above information

The mean is

`= n * p`

`= 40* (1)/(5)`

= 8

Now the variance is

`= 40* (1)/(5) * (4)/(5)`

=
`(32)/(5)`

So, the standard deviation is

`= \sqrt{(32)/(5) }`

= 2.529

hence, the mean and the standard deviation is 8 and 2.529 respectively