StylesScenario: A students takes the following quiz by taking random guesses.QuizInstructions: Select the corresponding character to the corresponding number:Question #1:b)b) воc) 55d) 12e)56f) The answer is not included.Question #2:b)b) 81c) 55d) 72e)56f) The answer is not includedQuestion #3:b) 5b) B1) 5d) 72e)65f) The answer is not includedQuestion #4:a)b) 81c) 55d) 72e)65f) The answer is not includedQuestion #5:a)b) 11,c) 15,d) 72e)65The answer is not includedn FoCusHIF5.5.1 11 0 e) Find the mean, expected value, variance, and standard deviation of the above scenario.

Answered: e) Find the mean, expected value,…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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Styles
Scenario: A students takes the following quiz by taking random guesses.
Quiz
Instructions: Select the corresponding character to the corresponding number:
Question #1:
b)
b) во
c) 55
d) 12
e)56
f) The answer is not included.
Question #2:
b)
b) 81
c) 55
d) 72
e)56
f) The answer is not included
Question #3:
b) 5
b) B1
) 5
d) 72
e)65
f) The answer is not included
Question #4:
a)
b) 81
c) 55
d) 72
e)65
f) The answer is not included
Question #5:
a)
b) 11,
c) 15,
d) 72
e)65
The answer is not included
n FoCus
HIF
5.
5.
1 1
1 0

e) Find the mean, expected value, variance, and standard deviation of the above scenario.

Expert Solution

Step 1 : Given Information

Here in this scenario, student takes a random guesses on his quiz. The quiz contains 5 multiple choice questions with each of the question having 6 options. Exactly one of the 6 options is correct. Hence probability that the students chooses the correct answer is 1/6. And this is same for all the 5 questions.

Let we define, X be number of correct answers in the quiz.

We observe that,

The number of trials (number of questions in the quiz) are 5, which are fixed.
For each trial there are only two outcomes, either answer is correct or incorrect. Let us denote success as, question answered by the student is correct.
Each trial is independent of each other, since each question is answered independently.
The probability of success, P(success) = 1/6, is same for each trial.

That means, X satisfies all the required conditions of binomial distribution.

Hence X defined above follows a binomial distribution with number of trials, 5 and probability of success, 1/6.

The probability mass function for X is defined as,

$P (X = x) = (\begin{matrix} 5 \\ x \end{matrix}) {(\frac{1}{6})}^{x} {(1 - \frac{1}{6})}^{5 - x}; x = 0, 1, 2, 3, 4, 5 . w h e r e (\begin{matrix} n \\ x \end{matrix}) = \frac{n!}{x! * (n - x)!}$

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