STAT 200 Fall 2015 Quiz #2 Please answer all 12 questions. The maximum score for each question is posted at the beginning of the question, and the maximum score for the quiz is 80 points. Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with necessary tables, if applicable. Answers that come straight from program software packages will not be accepted. Quizzes submitted after the due date will receive a grade of zero (0). IMPORTANT: Per the direction of the Dean's Office, you are requested to include a brief note at the beginning of your submitted quiz, confirming that your work is your own. By typing my signature below, I pledge that this is my own work done in accordance with the UMUC Policy 150.25 - Academic Dishonesty and Plagiarism (http://www.umuc.edu/policies/academicpolicies/aa15025.cfm) on academic dishonesty and plagiarism. I have not received or given any unauthorized assistance on this assignment/examination. _________________________ Electronic Signature Your submitted quiz will be accepted only if you have included this statement. 1. (10 points) Once upon a time, I had a fast-food lunch with a mathematician colleague. I noticed a very strange behavior in him. I called it the Au-Burger Syndrome since it was discovered by me at a burger joint. Based on my unscientific survey, it is a rare but real malady inflicting 2% of mathematicians worldwide. Yours truly has recently discovered a screening test for this rare malady, and the finding has just been reported to the International Association of Insane Scientists (IAIS) for publication. Unfortunately, my esteemed colleagues who reviewed my submitted draft discovered that the reliability of this screening test is only 80%. What it means is that it gives a positive result, false positive, in 20% of the mathematicians tested even though they are not afflicted by this horribly-embarrassing malady. I have found an unsuspecting victim, oops, I mean subject, down the street. This good old mathematician is tested positive! What is the probability that he is actually inflicted by this rare disabling malady? 2. (5 points) Most of us love Luzon mangoes, but hate buying those that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 15% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12? 3. (5 points) We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance tea.

1. STAT 200
Fall 2015
Quiz #2
Please answer all 12 questions. The maximum score for each
question is posted at the
beginning of the question, and the maximum score for the quiz
is 80 points. Make sure
your answers are as complete as possible and show your
work/argument. In particular,
when there are calculations involved, you should show how you
come up with your answers
with necessary tables, if applicable. Answers that come straight
from program software
packages will not be accepted. Quizzes submitted after the due
date will receive a grade of
zero (0).
IMPORTANT: Per the direction of the Dean's Office, you are
requested to include

2. a brief note at the beginning of your submitted quiz, confirming
that your work is
your own.
By typing my signature below, I pledge that this is my own
work done in
accordance with the UMUC Policy 150.25 - Academic
Dishonesty and Plagiarism
(http://www.umuc.edu/policies/academicpolicies/aa15025.cfm)
on academic
dishonesty and plagiarism. I have not received or given any
unauthorized
assistance on this assignment/examination.
_________________________ Electronic
Signature
Your submitted quiz will be accepted only if you have included
this statement.
1. (10 points) Once upon a time, I had a fast-food lunch with a
mathematician colleague. I
noticed a very strange behavior in him. I called it the Au-
Burger Syndrome since it was
discovered by me at a burger joint. Based on my unscientific
survey, it is a rare but real

3. malady inflicting 2% of mathematicians worldwide. Yours truly
has recently discovered a
screening test for this rare malady, and the finding has just been
reported to the International
Association of Insane Scientists (IAIS) for publication.
Unfortunately, my esteemed
colleagues who reviewed my submitted draft discovered that the
reliability of this screening
test is only 80%. What it means is that it gives a positive
result, false positive, in 20% of the
mathematicians tested even though they are not afflicted by this
horribly-embarrassing
malady.
I have found an unsuspecting victim, oops, I mean subject,
down the street. This good old
mathematician is tested positive! What is the probability that
he is actually inflicted by this rare
disabling malady?
2. (5 points) Most of us love Luzon mangoes, but hate buying
those that are picked too early.
Unfortunately, by waiting until the mangos are almost ripe to

4. pick carries a risk of having
15% of the picked rot upon arrival at the packing facility. If the
packing process is all done
by machines without human inspection to pick out any rotten
mangos, what would be the
probability of having at most 2 rotten mangos packed in a box
of 12?
3. (5 points) We have 7 boys and 3 girls in our church choir.
There is an upcoming concert in
the local town hall. Unfortunately, we can only have 5 youths
in this performance. This
performance team of 5 has to be picked randomly from the crew
of 7 boys and 3 girls.
a. What is the probability that all 3 girls are picked in this team
of 5?
b. What is the probability that none of the girls are picked in
this team of 5?
c. What is the probability that 2 of the girls are picked in this
team of 5?
4. (10 points) In this economically challenging time, yours
truly, CEO of the Outrageous
Products Enterprise, would like to make extra money to support
his frequent filet-mignon-

5. anddouble-lobster-tail dinner habit. A promising enterprise is
to mass-produce tourmaline
wedding rings for brides. Based on my diligent research, I have
found out that women's ring
size normally distributed with a mean of 6.0, and a standard
deviation of 1.0. I am going to
order 5000 tourmaline wedding rings from my reliable Siberian
source. They will
manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5,
8.0, 8.5, 9.0, and 9.5. How
many wedding rings should I order for each of the ring size
should I order 5000 rings
altogether? (Note: It is natural to assume that if your ring size
falls between two of the above
standard manufacturing size, you will take the bigger of the
two.)
5. (5 points) A soda company want to stimulate sales in this
economic climate by giving
customers a chance to win a small prize for ever bottle of soda
they buy. There is a 20%
chance that a customer will find a picture of a dancing banana (
) at the bottom of the cap

6. upon opening up a bottle of soda. The customer can then
redeem that bottle cap with this
picture for a small prize. Now, if I buy a 6-pack of soda, what
is the probability that I will
win something, i.e., at least winning a single small prize?
6. (5 points) When constructing a confidence interval for a
population with a simple random
sample selected from a normally distributed population with
unknown σ, the Student
tdistribution should be used. If the standard normal distribution
is correctly used instead, how
would the confidence interval be affected?
7. (10 points) Below is a summary of the Quiz 1 for two
sections of STAT 225 last spring. The
questions and possible maximum scores are different in these
two sections. We notice that
Student A4 in Section A and Student B2 in Section B have the
same numerical score.
Section A
Student Score

7. Section B
Student Score
A1 70 B1 15
A2 42 B2 61
A3 53 B3 48
A4 61 B4 90
A5 22 B5 85
A6 87 B6 73
A7 59 B7 48
----- ------ B8 39
How do these two students stand relative to their own classes?
And, hence, which student
performed better? Explain your answer.
8. (5 points) My brother wants to estimate the proportion of
Canadians who own their house.
What sample size should be obtained if he wants the estimate to
be within 0.02 with 90%
confidence if

8. a. he uses an estimate of 0.675 from the Canadian Census
Bureau?
b. he does not use any prior estimates? But in solving this
problem, you are actually using a
form of "prior" estimate in the formula used. In this case, what
is your "actual" prior
estimate? Please explain.
9. (5 points) An amusement park is considering the
construction of an artificial cave to attract
visitors. The proposed cave can only accommodate 36 visitors
at one time. In order to give
everyone a realistic feeling of the cave experience, the entire
length of the cave would be
chosen such that guests can barely stand upright for 98% of the
all the visitors.
The mean height of American men is 70 inches with a
standard deviation of 2.5 inches. An
amusement park consultant proposed a height of the cave based
on the 36-guest-at-a-time
capacity. Construction will commence very soon.
The park CEO has a second thought at the last minute, and
asks yours truly if the proposed

9. height is appropriate. What would be the proposed height of the
amusement park consultant?
And do you think that it is a good recommendation? If not,
what should be the appropriate
height? Why?
10.(5 points) A department store manager has decided that
dress code is necessary for team
coherence. Team members are required to wear either blue
shirts or red shirts. There are 9
men and 7 women in the team. On a particular day, 5 men wore
blue shirts and 4 other wore
red shirts, whereas 4 women wore blue shirts and 3 others wore
red shirt. Apply the Addition
Rule to determine the probability of finding men or blue shirts
in the team.
Please refer to the following information for Question 11 and
12.
It is an open secret that airlines overbook flights, but we have
just learned that bookstores
underbook (I might have invented this new term.) textbooks in
the good old days that we had to
purchase textbooks.

10. To make a long story short, once upon a time, our UMUC
designated virtual bookstore, MBS
Direct, routinely, as a matter of business practice, orders less
textbooks than the amount
requested by UMUC's Registrar's Office. That is what I have
figured out....... Simply put, MBS
Direct has to "eat" the books if they are not sold. Do you want
to eat the books? You may want
to cook the books before you eat them! Oops, I hope there is no
account major in this class?
OK, let us cut to the chase..... MBS Direct believes that only
85% of our registered students
will stay registered in a class long enough to purchase the
required textbook. Let's pick on our
STAT 200 students. According to the Registrar's Office, we
have 600 students enrolled in STAT
200 this spring 2014.
11. (10 points) Suppose you are the CEO of MBS Direct, and
you want to perform a
probability analysis. What would be the number of STAT 200
textbook bundles you would
order so that you stay below 5% probability of having to back-
order from Pearson Custom

11. Publishing? (Note: Our Provost would be very angry when she
hears that textbook bundles have
to be backordered. In any case, we no longer need the service
of MBS Direct as we are moving
to 100% to free eResources. Auf Wiedersehen, MBS
Direct......)
IMPORTANT: Yes, you may use technology for tacking
Question 11 in this quiz.
12. (5 points) Is there an approximation method for Question
11? If so, please tackling
Question 11 with the approximation method.