Question

A multiple choice test has four possible answers for each question. Let X be the number of correct responses in a test of 100 questions if the student simply guesses on each question. The standard deviation of X is

a. 4.33.
b. 18.75.
c. 0.433.

Answer 1

a. 4.33.

Explanation:

If there is only one correct answer out of four alternatives, the expected proportion of correct answers is p =0.25

Sample size (n) = 100 questions

The standard deviation of a proportion 'p' is given by:

`s=\sqrt{(p*(1-p))/(n) }`

Applying the given data:

`s=\sqrt{(0.25*(1-0.25))/(100)}\\s=0.0433`

If X is the number of correct responses in 100 guesses, the standard deviation of X is:

`\sigma = n*s=100*0.0433\\\sigma = 4.33`

The standard deviation of X is 4.33 questions.