Question

On a multiple choice test with 13 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.
Select one:
A. 1.875.
B. 1.53.
C. 1.47.
D. 1.5.
E. 1.561.

Answer 1

Answer: E. 1.561.

Step-by-step explanation:

Given, Total choices for each question =4

Probability that a particular answer is correct : p = $\dfrac{1}{4}=0.25$

Sample size : n= 13

Formula for standard deviation: $\sigma=\sqrt{np(1-p)}$

Put all values, we get

$\sigma=\sqrt{13(0.25)(1-0.25)}=\sqrt{13(0.25)(0.75)}$

$\sigma=\sqrt{2.4375}\approx1.561$

Hence, the standard deviation is 1.561.

So, the correct option is E.