STAT 225 Section 6380 Summer 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. The quiz is due by midnight, Sunday, June 28, Eastern Daylight Saving Time. 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. http://www.umuc.edu/policies/academicpolicies/aa15025.cfm http://www.umuc.edu/policies/academicpolicies/aa15025.cfm 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 .

1. STAT 225
Section 6380
Summer 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. The quiz is due by midnight,
Sunday, June 28, Eastern
Daylight Saving Time.
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

2. 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.
http://www.umuc.edu/policies/academicpolicies/aa15025.cfm
http://www.umuc.edu/policies/academicpolicies/aa15025.cfm
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

3. 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 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. 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-and-
double-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.)
http://polaris.umuc.edu/%7Eaau/crying_baby.html
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 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

5. 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 t-
distribution 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
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

6. 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
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

7. 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
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

8. purchase textbooks.
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 Publishing? (Note:
Our Provost would be very angry when she hears that textbook
bundles have to be back-
ordered. 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......)

9. 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.