Question

A multiple-choice test consists of 20 items, each with four choices. A student is able to eliminate one of the choices on each question as incorrect and chooses randomly from the remaining three choices. A passing grade is 12 items or more correct. Let X be the number of questions the student answers correctly.

a) What is the pdf of X?

b) What is the probability that the student passes?

c)What is the E(X) & Var(X)?

d)What is the m.g.f of X?

Answer #1

**Solution:** The given process (number of
questions the student answers correctly) follows the binomial
distribution with n=20 and probability of succes
.

a) What is the pdf of X?

**Answer:** Since X follows Binomial distribution,
therefore the pdf of X is given below:

b) What is the probability that the student passes?

**Answer:** A student passes if he/she answers 12
or more correct. Therefore the probability that the student passes
is

Therefore the probability that the student passes is
**0.01297**

c)What is the E(X) & Var(X)?

**Answer:
**

** **

d)What is the m.g.f of X?

**Answer:** The m.g.f of binomial distribution is
given below:

Therefore the m.g.f is

a multiple choice quiz in six sigma green belt 11 consists of 10
questions each of which has five possible answers of which only one
is correct. a student passes the quiz if six or more correct answer
obtained. what is the probability of passing the quiz if on each
question, a student can eliminate three incorrect answers and then
guess between the remaining two.

A quiz consists of 15 multiple-choice questions. Each question
has 5 choices, with exactly one correct choice. A student, totally
unprepared for the quiz, guesses on each of the 15 questions. a.
How many questions should the student expect to answer correctly?
b. What is the standard deviation of the number of questions
answered correctly? c. If at least 7 questions must be answered
correctly to pass the quiz, what is the chance the student
passes?

A multiple-choice test consists of 7 questions. Each question
has answer choices of a, b, c, and d, and only one of the choices
is correct. If a student randomly guesses on each question, what is
the probability that he gets fewer than 2 of them correct?

A multiple-choice test consists of eight questions, each of
which has four choices. Each question has exactly one correct
answer.
William guesses randomly at each answer. What is the probability
that he gets six or fewer questions correct? (Round your answer to
four decimal places.)

2. A multiple-choice test has 25 questions. There are four
choices for each question. A student who has not studied for the
test decides to answer all questions by randomly choosing one of
the four choices. What probability distribution can be used to
compute his chance of correctly answering at least 15
questions?
a. Normal distribution b. Binomial distribution c. Poisson
distribution d. None of these

A multiple-choice test consists of 10 questions. Each question
has answer choices of a, b, c,
d, and e, and only one of the choices is correct.
If a student randomly guesses on each question, what is the
probability that he gets at most 1 of them correct?
Carry your intermediate computations to at least four decimal
places, and round your answer to at least two decimal places.

A multiple-choice test has four questions, each with five
choices for the answer. Only one of the choices is correct. You
randomly guess the answer to each question. What is the probability
that you answered at least one questions correctly?
A. 0.5904
B.0.1808
C.0.216
D. 0.8192

Suppose in a multiple choice type test, each question has five
choices. To discourage students from guessing the correct answer,
the following scoring method is used: 7 points for correct answer,
0 point for wrong answer, and 2 points for leaving the question
unanswered. What is the minimum number of choices
in each question a student should be able to eliminate, so that it
becomes advantageous to guess from the remaining choices?
choice: 1 2 3 4

2. You are taking a 33 question multiple choice test, each
question with 4 choices. Assume that getting 23 questions or more,
correct, will result in a passing grade on the test. Complete parts
(a), (b), and (c).
(a) If you randomly guess on a single question, what is the
probability that you will get that question correct?
(b) If you randomly guess on all 33 questions, what is the
probability that you will pass?
(c) About what number of...

On Excel, A multiple choice test has 30
problems, and 4 choices for each problem. A student taking the test
does not know the correct answer for any of the problems and
guesses each answer. What is the probability that the student will
answer at least 10 questions correctly?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 25 minutes ago

asked 29 minutes ago

asked 48 minutes ago

asked 54 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago