Question

A multiple-choice test consists of 25 questions, each with four possible answers. If our desperate business statistics student answers the test by guessing the answers before reading the questions (that is, by selecting an answer at random for each question), use the normal curve approximation to find the probabilities that he will get:

exactly six correct answers (b) at least seven correct answers

fewer than four correct answers (d) more than two, but fewer than nine correct answers

What is the probability of getting at least 12 replies to questionnaires mailed to 100 persons, when the probability is 0.18 that any one of them will reply?

Answer #1

n = 25

P = 0.25

= n * P = 25 * 0.25 = 6.25

= sqrt(n * P * (1 - P))

= sqrt (25 * 0.25 * 0.75) = 4.6875

a) P(X = 6)

= P(5.5 < X < 6.5)

= P((5.5 - )/< (X - )/< (6.5 - )/)

= P((5.5 - 6.25)/4.6875 < Z < (6.5 - 6.25)/4.6875)

= P(-0.16 < Z < 0.05)

= P(Z < 0.05) - P(Z < -0.16)

= 0.5199 - 0 .4364

= 0.0835

B) P(X > 7)

= P(X > 6.5)

= P((X - )/> (6.5 - )/)

= P(Z > (6.5 - 6.25)/4.6875)

= P(Z > 0.05)

= 1 - P(Z < 0.05)

= 1 - 0.5199

= 0.4801

C) P(X < 4)

= P(X < 3)

= P(X < 3.5)

= P((X - )/< (3.5 - )/)

= P(Z < (3.5 - 6.25)/4.6875)

= P(Z < -0.59)

= 0.2776

D) P(2 < X < 9)

= P(3 < X < 8)

= P(2.5 < X < 8.5)

= P((2.5 - )/< (X - )/< (8.5 - )/)

=P((2.5 - 6.25)/4.6875 < Z < (8.5 - 6.25)/4.6875)

= P(-0.8 < Z < 0.48)

= P(Z < 0.48) - P(Z < -0.8)

= 0.6844 - 0.2119

= 0.4725

A multiple-choice test consists of 27 questions with possible
answers of a, b, c, d, e, f. Estimate the probability that with
random guessing, the number of correct answers is at least 8.

A multiple choice test consists of 23 questions with possible
answers of a,b,c,d. Estimate the probability that with random
guessing the number of correct answers is at least 11.

If you make random guesses for 20 multiple choice test questions
each with four possible answers, what is the probability of
a) Getting at least one correct (5 points)
b) Getting all
answers wrong; (5 points)

A multiple-choice exam has 80 questions, each with four possible
answers. If a student is just guessing at all the answers, the
probability that he or she gets at least 30
correct is closest to?
A.0.2
B.0.008
C.0.1
D.0.025

MC1701: A test consists of 10 multiple choice questions, each
with five possible answers, one of which is correct. To pass, a
student must get at least 6 correct on the test. If a student
randomly guesses at every question, what is the probability that
the student fails the test?
a.
2.6%
b.
20%
c.
80%
d.
97.4%
e.
99.4%
f.
None of these

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.)

A test consists of 10 multiple choice questions, each with five
possible answers, one of which is correct. To pass the test a
student must get 60% or better on the test. If a student randomly
guesses, what is the probability that the student will pass the
test? Please show work

A multiple choice exam consists of 25 questions, each with 4
possible answers. Suppose that a student doesn't know the material
and simply guesses on each question.
Using the CDF command in MINITAB, answer the following
questions.
1) What is the probability that they get at least 13 questions
correct?
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
0.9-1.0

1. a test consists of 25 multiple choice questions with 5
possible answers, only 1 of which is correct. find the mean and
standard deviation. ( binomial)
2. Duchess county , N.Y, has been experiencing a mean of 35.4
motor vehicle deaths each year.
a. find the mean number of deaths per day. (poisson)
b. find the probability that on a given day, there are more than
2 motor vehicle deaths

Q3) A multiple choice test contains 25 questions each with four
answers. Assume a student just guess on each question.
i. What is the expected number of the correct answers?
ii. What is the probability that the student answers more than
20 questions?

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