Problem 3CQQ

Using the same SAT questions described in Exercise, find the standard deviation for the numbers of correct answers for those who make random guesses for all 100 questions.

Exercise

There are 100 questions from an SAT test, and they are all multiple choice with possible answers of a, b, c, d, e. For each question, only one answer is correct. Find the mean number of correct answers for those who make random guesses for all 100 questions.

Problem 3CQQ

Answer:

Step1 of 2:

We have There are 100 questions from an SAT test, and they are all multiple choice with possible answers of a, b, c, d, e. For each question, only one answer is correct. We need to find the mean number of correct answers for those who make random guesses for all 100 questions.

Here,

n = 100

S = {a,b,c,d,e}

Probability of getting correct answer P(correct) = ⅕

Hence p = ⅕

Step2 of 2:

The mean number of correct answers for those who make random guesses for all 100 questions is given by

E(x) = np

= 1000.20

= 20

Therefore,E(x) = 20

var(x) = npq

= 1000.200.8

= 16

The standard deviation of correct answers for those who make random guesses for all 100 questions is given by

Standard deviation is given by =

=

= 4.