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

Answer:

8 and 2.529

Step-by-step 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 =  $\frac{1}{5}$

So, the probability of the wrong answer is q =  $1 - \frac {1}{5}$ = $\frac{4}{5}$

Moreover, this is the binomial distribution

Based on the above information

The mean is

$= n \times p$

$= 40\times \frac{1}{5}$

= 8

Now the variance is

$= 40\times \frac{1}{5} \times \frac{4}{5}$

= $\frac{32}{5}$

So, the standard deviation is

$= \sqrt{\frac{32}{5} }$

= 2.529

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