Question

On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. a. 12.8.b. 8.5.c. 4.3.d. 5.7.

Answer 1

The required "option c) 4.3" is correct.

Step-by-step explanation:

Given,

Total number of multiple choice questions = 17

To find, the mean for the number of correct answers = ?

Each question has four possible answers.

If guessing at random:

There is only one in four chances.

$\dfrac{1}{4}\times 100$ =  25 % chance of getting a particular question right.

This is the same probability for each of the 17 questions.

If there is a 25 % chance of getting any given question right.

There are 17 questions.

∴ The total number of questions you will expect to get right =

25 %  × 17

= $\dfrac{25}{100} \times 17$

= $\dfrac{17}{4}$

= 4.25

≈ 4.3

∴ The mean for the number of correct answers = 4.3

Thus, the required "option c) 4.3" is correct.