# STAT 200 Quiz 2

$20.00

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 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-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 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

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

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

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.

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 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 tackle Question

11 with the approximation method

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 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-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 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

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

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

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.

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 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 tackle Question

11 with the approximation method