Question

Section II – During finals week, some instructors tend to use
multiple-choice (A, B, C, or D) **and** true/false
questions on the exam. Let us continue working with multiple-choice
problems, but let us say instead that the instructor has
**eight (8)** multiple-choice problems with
***four possible choices*** for each problem. Use this
information for all problems on this page!

What are the four requirements for an experiment to be a binomial experiment?

Do the eight multiple-choice questions satisfy those requirements? Explain your answer.

What is the probability of obtaining exactly 5 correct answers?

What is the probability of obtaining at least 5 correct answers?

What is the probability of obtaining at most 6 correct answers?

Answer #1

The four requirements for an experiment to be a binomial experiment :

- number of trials is fixed . in this case n = 8
- There are only two possible outcomes in each trial - a correct answer or a incorrect answer
- The probability of answering each questions correctly does not depend on other questions.
- The probability of correctly answering each question is fixed, one of the four options is correct, so

So, X ~ Binomial( n = 8, p = 0.25)

The probability mass function of X is

Now,

The probability of obtaining exactly 5 correct answers

The probability of obtaining at least 5 correct answers

c) The probability of obtaining at most 6 correct answers

Jimmy has a quiz today that is multiple choice (a, b, c, or d)
with ten questions, but he did not study, so he decides to randomly
mark answers on his scantron without reading the questions.
a) Why should the number of questions Jimmy gets correct on the
quiz follow a binomial distribution, to wit, what are the
requirements to use a binomial distribution and how are they met in
this scenario?
b) List the parameters that define this distribution...

A multiple choice test consisting of 10 questions. each question
has four choices. a,b,c, and d tell how you would find the
probability of guessing at least one correct answer, without the
use of binomial probability formula. what rule would your use to
simplify your solution?

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B
C...

Answers to Multiple-Choice Problems: A student
wants to see if the correct answers to multiple choice problems are
evenly distributed. She heard a rumor that if you don't know the
answer, you should always pick C. In a sample of 100
multiple-choice questions from prior tests and quizzes, the
distribution of correct answers are given in the table below. In
all of these questions, there were four options {A, B, C, D}.
Correct Answers (n = 100)
A
B
C...

Multiple Choice Strategy: Some students have
suggested that if you have to guess on a multiple-choice question,
you should always choose C. Carl, the student, wants to
investigate this theory. He is able to get a sample of past tests
and quizzes from various teachers. In this sample there are 110
multiple-choice questions with four options (A, B, C, D).
The distribution of correct answers from this sample is given in
the frequency table below.
Correct
Answer
Frequency
A
21...

Multiple Choice Strategy: Some students have
suggested that if you have to guess on a multiple-choice question,
you should always choose C. Carl, the student, wants to
investigate this theory. He is able to get a sample of past tests
and quizzes from various teachers. In this sample there are 90
multiple-choice questions with four options (A, B, C, D).
The distribution of correct answers from this sample is given in
the frequency table below.
Correct Answer
Frequency
A
17...

Multiple Choice Strategy: Some students have
suggested that if you have to guess on a multiple-choice question,
you should always choose C. Carl, the student, wants to
investigate this theory. He is able to get a sample of past tests
and quizzes from various teachers. In this sample there are 90
multiple-choice questions with four options (A, B, C, D).
The distribution of correct answers from this sample is given in
the frequency table below.
Correct
Answer
Frequency
A
16...

On a certain statistics exam, there are 9 multiple choice
questions. Each question has 5 possible answers to choose from (and
only 1 correct answer). Suppose you didn’t study at all and are
planning on guessing the correct answer for each question.
Therefore, the probability of guessing a question correctly is
___________ . (Round to two decimals)
Let X = number of questions the student guesses
correctly
(Round all answers to four decimals)
a) What’s the probability you
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Richard has just been given a 8-question multiple-choice quiz in
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doesn't know any of the answers. Assuming that Richard guesses on
all eight questions, find the indicated probabilities. (Round your
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(b) What is the probability that he will answer all questions...

The Auditing and Attestation (AUD) part of the CPA exam has 72
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What is P(G≥38)? P(16<G≤35)?
P(G≤30)? If appropriate, use the approximation of a binomial to
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