Answer:
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;
[tex]P(X = x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,......[/tex]
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 = [tex]\frac{1}{5}[/tex] = 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) = [tex]n \times p[/tex]
= [tex]15 \times 0.2[/tex] = 3
And the standard deviation of the number of correct answers is given by;
Standard deviation, S.D.(X) = [tex]\sqrt{n \times p\times (1-p)}[/tex]
= [tex]\sqrt{15 \times 0.2\times (1-0.2)}[/tex] = 1.55
