Download Winter 2014 Exam 2

Winter 2014 FORM A
Name Last:_________________ First: _______________
Exam 2: Chapters 4, 5, 6 & 7
Class Time:________________________
Directions:
• Print your NAME and CLASS TIME on THIS EXAM
• Print your NAME and CLASS TIME on your SCANTRON.
• Write FORM A on your SCANTRON.
• Turn your cell phone OFF. Any noise from a cell phone will signal that your exam is over.
• Each question has exactly one BEST answer. There are 21 questions.
• You may write on this exam. There is no scratch paper allowed.
• Each question is worth 5 points for a total of 105 points.
• If you have no note page, you must write NO NOTES on your SCANTRON.
• Put your SCANTRON and PAGE of NOTES inside your EXAM. Before you start packing up your
things, turn in your EXAM and SCANTRON. Then go back to your desk to pack up your materials.
When your exam is returned, you will get back all your materials.
•
FAILURE TO FOLLOW ALL INSTRUCTIONS COULD COST YOU 5 POINTS!
__________________________________________________________________________________________________
Use the following information for questions 1 – 3
After bacteria are subjected to a certain drug, the length of time until the bacteria die follows an exponential
distribution with a mean of 0.5 hour.
1. How long after the drug is administered will 40% of the bacteria be dead?
A. 0.458 hours
B. 0.255 hours
C. 1.022 hours
D. 1.833 hours
2. What is the probability that the time it takes for the bacteria to die is between 0.2 and 0.8 hour?
A. 0.5316
B. 0.2345
C. 0.7655
D. 0.4684
3. Which of the following statements is/are true?
I. The mean lifetime of the bacteria is less than the median lifetime of the bacteria.
II. The mean and the standard deviation are the same.
III. The distribution is not symmetrical.
A. I,II and III
B. I, II
C. II, III
D. I, III
Use the following information for questions 4 - 6
At a factory, soft drink bottles are filled with soda. The amount of soda in the bottles is normally distributed
with mean 1 liter and standard deviation of 0.05 liters.
4. What proportion of the bottles contain between 0.95 and 1.05 liters?
A. 0.3173
B. 0.6827
C. 0.1587
D. 0.8413
5. What is the expected amount of soda in a bottle, in liters?
A. Between 0.95 and 1.05
B. 0.05
C. 1
D. Unable to determine
6. Find the 85th percentile for the amount of soda in a bottle at this factory.
A. 1.0518
B. 0.0013
C. 0.9482
D. 0.9987
Use the following information for questions 7 - 9
A recent Field Poll conducted April 6, 2006 showed that 60% of California registered voters favor creating a
temporary worker program for illegal immigrants that would legalize their status and allow future immigrants to
work in the United States. Suppose that 25 California registered voters are randomly chosen. Let X = the
number who favor creating a temporary worker program for illegal immigrants.
7. What is the probability that at least 15 of the randomly chosen California registered voters are in favor of a
temporary worker program for illegal immigrants?
A. 0.4142
B. 0.4246
C. 0.5753
D. 0.5858
8. What is the probability that exactly 20 of the randomly chosen California registered voters are in favor of
a temporary worker program for illegal immigrants?
A. 0.9905
B. 0.0199
C. 0.0383
D. 0.0095
9. How many of the 25 randomly chosen California registered voters would we expect to favor creating a
temporary worker program for illegal immigrants?
A. 0.60
B. 25
C. 15
D. Unable to determine
10. Which of the following distributions is described by the following example?
In a collector’s collection of CDs, the times each song lasts is equally likely to be between 2 and 3.5 minutes.
A. Binomial
B. Normal
C. Uniform
D. Exponential
Use the following information for questions 11 - 13
Suppose the lifetime of a certain kind of battery is exponentially distributed, with an average of 40 hours. We
are interested in the average lifetime of 16 of these batteries.
11. What is the distribution for the average lifetime of 16 of these batteries?
A. Exp(1/40)
B. N(40,10)
C. N(40,40)
D. Exp(40)
12. Find the probability that the average lifetime of 16 batteries is between 35 and 40 hours.
A. 0.0490
B. 0.9510
C. 0.0497
D. 0.1915
13. Find the 75th percentile for the average lifetime of 16 batteries in hours.
A. 46.74
B. 66.98
C. 55.45
D. 11.51
Use the following information for questions 14 - 16
The time to wait for an Amtrak train is distributed uniformly from 0 to 48 minutes.
14. The distribution to use is:
A. U(0,48)
B. Exp (1/24)
C. N(24, 13.86)
D. N(24, 1.55)
C. 0.875
D. 0.8542
15. The probability the time to wait will be more than 6 minutes is:
A. 0.1458
B. 0.125
16. Interpret the 90th percentile for the time to wait for an Amtrak train:
A.
B.
C.
D.
90% of the wait times will be at least 4.8 minutes.
90% of the wait times will be at most 4.8 minutes.
90% of the wait times will be at least 43.2 minutes.
90% of the wait times will be at most 43.2 minutes.
Use the following information for questions 17 - 18
People visiting the City Library often check out more than one book at a time. The probability distribution for
books checked out per person at the City Library is given below. There is a six-book limit per person at this
library, so nobody ever checks out more than six books.
Number of Books
checked out
P(X = x)
Library Books
0
0.15
1
2
3
4
5
6
0.25
0.40
0.12
0.04
0.02
0.02
17. What is the expected number of books checked out per person?
A. 1.79
B. 3
C. 3.5
D. 2.79
18. If the library has 120 people visit it on Monday, what is the expected number of books checked out on
Monday?
A. 360
B. 334.8
C. 214.8
D. 420
19. Ejection Seats in Fighter Jets. Suppose the weight of women in the US is modeled by a normal distribution
with mean 143 pounds and standard deviation 29 pounds. Ejection seats in fighter jets are designed for people
weighing between 110 and 170 pounds. What percentage of women in the US are outside of this weight range?
A. 30.35
B. 69.65
C. 75.74
D. 24.26
Use the following for questions 20 and 21.
Suppose De Anza students have an average age of 27 with a standard deviation of 6.2 years. If we take a
random sample of 100 De Anza students and compute the average age of the sampled students, then
20. In words, X-bar =
A. Age, in years, for one De Anza student.
B. Age, in years, for 100 De Anza students.
C. Average age, in years, for one De Anza student.
D. Average age, in years, for 100 De Anza students.
21. How does the graph of X-bar compare to X?
A.
B.
C.
D.
X-bar is more peaked than X and has the same average as X.
X-bar is more peaked than X and is shifted to the left of X.
X-bar is flatter than X and has the same average as X.
X-bar is more peaked than X and is shifted to the right of X.
Winter 2014 FORM B
Name Last:_________________ First: _______________
Exam 2: Chapters 4, 5, 6 & 7
Class Time:________________________
Directions:
• Print your NAME and CLASS TIME on THIS EXAM
• Print your NAME and CLASS TIME on your SCANTRON.
• Write FORM B on your SCANTRON.
• Turn your cell phone OFF. Any noise from a cell phone will signal that your exam is over.
• Each question has exactly one BEST answer. There are 21 questions.
• You may write on this exam. There is no scratch paper allowed.
• Each question is worth 5 points for a total of 105 points.
• If you have no note page, you must write NO NOTES on your SCANTRON.
• Put your SCANTRON and PAGE of NOTES inside your EXAM. Before you start packing up your
things, turn in your EXAM and SCANTRON. Then go back to your desk to pack up your materials.
When your exam is returned, you will get back all your materials.
•
FAILURE TO FOLLOW ALL INSTRUCTIONS COULD COST YOU 5 POINTS!
__________________________________________________________________________________________________
Use the following information for questions 1 - 3
Suppose the lifetime of a certain kind of battery is exponentially distributed, with an average of 40 hours. We
are interested in the average lifetime of 16 of these batteries.
1. What is the distribution for the average lifetime of 16 of these batteries?
A. Exp(1/40)
B. N(40,10)
C. N(40,40)
D. Exp(40)
2. Find the probability that the average lifetime of 16 batteries is between 35 and 40 hours.
A. 0.0490
B. 0.9510
C. 0.0497
D. 0.1915
3. Find the 75th percentile for the average lifetime of 16 batteries in hours.
A. 46.74
B. 66.98
C. 55.45
D. 11.51
4. Which of the following distributions is described by the following example?
In a collector’s collection of CDs, the times each song lasts is equally likely to be between 2 and 3.5 minutes.
A. Binomial
B. Normal
C. Uniform
D. Exponential
Use the following information for questions 5 - 6
People visiting the City Library often check out more than one book at a time. The probability distribution for
books checked out per person at the City Library is given below. There is a six-book limit per person at this
library, so nobody ever checks out more than six books.
Number of Books
checked out
P(X = x)
Library Books
0
0.15
1
2
3
4
5
6
0.25
0.40
0.12
0.04
0.02
0.02
5. What is the expected number of books checked out per person?
A. 1.79
B. 3
C. 3.5
D. 2.79
6. If the library has 120 people visit it on Monday, what is the expected number of books checked out on
Monday?
A. 360
B. 334.8
C. 214.8
D. 420
Use the following information for questions 7 - 9
After bacteria are subjected to a certain drug, the length of time until the bacteria die follows an exponential
distribution with a mean of 0.5 hour.
7. How long after the drug is administered will 40% of the bacteria be dead?
A. 0.458 hours
B. 0.255 hours
C. 1.022 hours
D. 1.833 hours
8. What is the probability that the time it takes for the bacteria to die is between 0.2 and 0.8 hour?
A. 0.5316
B. 0.2345
C. 0.7655
D. 0.4684
9. Which of the following statements is/are true?
I. The mean lifetime of the bacteria is less than the median lifetime of the bacteria.
II. The mean and the standard deviation are the same.
III. The distribution is not symmetrical.
A. I,II and III
B. I, II
C. II, III
D. I, III
Use the following for question 10 and 11.
Suppose De Anza students have an average age of 27 with a standard deviation of 6.2 years. If we take a
random sample of 100 De Anza students and compute the average age of the sampled students, then
10. In words, X-bar =
A. Age, in years, for one De Anza student.
B. Age, in years, for 100 De Anza students.
C. Average age, in years, for one De Anza student.
D. Average age, in years, for 100 De Anza students.
11. How does the graph of X-bar compare to X?
A.
B.
C.
D.
X-bar is more peaked than X and has the same average as X.
X-bar is more peaked than X and is shifted to the left of X.
X-bar is flatter than X and has the same average as X.
X-bar is more peaked than X and is shifted to the right of X.
Use the following information for questions 12 - 14
A recent Field Poll conducted April 6, 2006 showed that 60% of California registered voters favor creating a
temporary worker program for illegal immigrants that would legalize their status and allow future immigrants to
work in the United States. Suppose that 25 California registered voters are randomly chosen. Let X = the
number who favor creating a temporary worker program for illegal immigrants.
12. What is the probability that at least 15 of the randomly chosen California registered voters are in favor of a
temporary worker program for illegal immigrants?
A. 0.4142
B. 0.4246
C. 0.5753
D. 0.5858
13. What is the probability that exactly 20 of the randomly chosen California registered voters are in favor of
a temporary worker program for illegal immigrants?
A. 0.9905
B. 0.0199
C. 0.0383
D. 0.0095
14. How many of the 25 randomly chosen California registered voters would we expect to favor creating a
temporary worker program for illegal immigrants?
A. 0.60
B. 25
C. 15
D. Unable to determine
15. Ejection Seats in Fighter Jets. Suppose the weight of women in the US is modeled by a normal distribution
with mean 143 pounds and standard deviation 29 pounds. Ejection seats in fighter jets are designed for people
weighing between 110 and 170 pounds. What percentage of women in the US are outside of this weight range?
A. 30.35
B. 69.65
C. 75.74
D. 24.26
Use the following information for questions 16 - 18
The time to wait for an Amtrak train is distributed uniformly from 0 to 48 minutes.
16. The distribution to use is:
A. U(0,48)
B. Exp (1/24)
C. N(24, 13.86)
D. N(24, 1.55)
17. The probability the time to wait will be more than 6 minutes is:
A. 0.1458
B. 0.125
C. 0.875
D. 0.8542
18. Interpret the 90th percentile for the time to wait for an Amtrak train:
A.
B.
C.
D.
90% of the wait times will be at least 4.8 minutes.
90% of the wait times will be at most 4.8 minutes.
90% of the wait times will be at least 43.2 minutes.
90% of the wait times will be at most 43.2 minutes.
Use the following information for questions 19 - 21
At a factory, soft drink bottles are filled with soda. The amount of soda in the bottles is normally distributed
with mean 1 liter and standard deviation of 0.05 liters.
19. What proportion of the bottles contain between 0.95 and 1.05 liters?
A. 0.3173
B. 0.6827
C. 0.1587
D. 0.8413
20. What is the expected amount of soda in a bottle, in liters?
A. Between 0.95 and 1.05
B. 0.05
C. 1
D. Unable to determine
21. Find the 85th percentile for the amount of soda in a bottle at this factory.
A. 1.0518
B. 0.0013
C. 0.9482
D. 0.9987
Answers
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
FORM A
B
D
C
B
C
A
D
B
C
C
B
D
A
A
C
D
A
C
A
D
A
FORM B
B
D
A
C
A
C
B
D
C
D
A
D
B
C
A
A
C
D
B
C
A