Introduction to Statistics - Theorem 2025/12/01, 21:14
INTRODUCTION TO STATISTICS
MTHH041055
Assignment
Unit 2 Evaluation
Review
Assignment Grade Assignment Weight
A+ 100% 7%
Date Submitted Date Graded
NOV 28, 2025 NOV 28, 2025
Terrific! You have done an exceptional job on this unit evaluation! By answering all of the questions correctly,
you have demonstrated your mastery of the material in Unit 2. You have learned a great deal summarizing and
graphing data. You have a good understanding of normal distribution and linear and curved models. Keep up
the excellent work!
After you have reviewed this report, complete Project 2, and then move on to Unit 3.
Unit 2 Evaluation (printable format) (/Files/Courses/MTHH041055/Unit-2/Unit-2-Evaluation/Unit
2 Evaluation (printable format).pdf)
Multiple Choice
Select the response that best completes the statement or answers the question.
1. What percent of cars have a fuel efficiency within 1σ of the mean?
A. 32%
B. 95%
C. 34%
D. 68%
Correct Answer: D
Apply the 68-95-99.7 Rule. By definition, 68% of data lies within 1σ of the mean. Review Chapter 5 in
Stats in Your World textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 1 of 26
,Introduction to Statistics - Theorem 2025/12/01, 21:14
2. What percent of cars have a fuel efficiency greater than 1σ above the mean?
A. 50%
B. 16%
C. 68%
D. 32%
Correct Answer: B
Apply the 68-95-99.7 Rule. By definition, 68% of data lies within 1σ of the mean. To find 1σ above the
mean subtract 68% from 100% and divide by 2; (100 – 68)/2 = 16%. Review Chapter 5 in Stats in Your
World textbook for more information.
3. What percent of cars have a fuel efficiency less than 2σ below the mean?
A. 2.5%
B. 5%
C. 95%
D. 99.7%
Correct Answer: A
Apply the 68-95-99.7 Rule. 95% of data is within2σ of the mean. That leaves 5% outside. Half of that is in
one tail; (100 – 5)/2 = 2.5%. Review Chapter 5 in Stats in Your World textbook for more information.
4. What percent of cars have a fuel efficiency between 1σ above the mean and 2σ above the mean?
A. 34%
B. 27%
C. 13.5%
D. 81.5%
Correct Answer: C
Apply the 68-95-99.7 Rule. 47.5% of data lie 2σ above the mean, while 34% lie 1σ above the mean.
Subtract to find the percent in between; (47.5 – 34) = 13.5%. Review Chapter 5 in Stats in Your World
textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 2 of 26
, Introduction to Statistics - Theorem 2025/12/01, 21:14
5. Use this information to answer questions 5-9. Suppose a normal model describes the fuel efficiency of cars
currently registered in your state. The mean is 29 MPG, with a standard deviation of 5 mpg.
What is the range of fuel efficiency for cars within 1σ of the mean?
A. 24 mpg – 34 mpg
B. 28 mpg – 30 mpg
C. 29 mpg – 34 mpg
D. −1 mpg – +1 mpg
Correct Answer: A
Apply the 68-95-99.7 Rule. Find the mean ±5 mpg; 29 − 5 and 29 + 5, 24 mpg – 34 mpg. Review
Chapter 5 in Stats in Your World textbook for more information.
6. What percent of all cars get less than 20 mpg?
A. 31.0%
B. 3.6%
C. 5.5%
D. 50%
Correct Answer: B
Find the z-score, z = (y – µ)/σ, (20 – 29)/5 = −1.80. Then the percent which corresponds to that z-score
by using Table Z; 0.0359 ≈ 3.6%. Review Chapter 5 in Stats in Your World textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 3 of 26
INTRODUCTION TO STATISTICS
MTHH041055
Assignment
Unit 2 Evaluation
Review
Assignment Grade Assignment Weight
A+ 100% 7%
Date Submitted Date Graded
NOV 28, 2025 NOV 28, 2025
Terrific! You have done an exceptional job on this unit evaluation! By answering all of the questions correctly,
you have demonstrated your mastery of the material in Unit 2. You have learned a great deal summarizing and
graphing data. You have a good understanding of normal distribution and linear and curved models. Keep up
the excellent work!
After you have reviewed this report, complete Project 2, and then move on to Unit 3.
Unit 2 Evaluation (printable format) (/Files/Courses/MTHH041055/Unit-2/Unit-2-Evaluation/Unit
2 Evaluation (printable format).pdf)
Multiple Choice
Select the response that best completes the statement or answers the question.
1. What percent of cars have a fuel efficiency within 1σ of the mean?
A. 32%
B. 95%
C. 34%
D. 68%
Correct Answer: D
Apply the 68-95-99.7 Rule. By definition, 68% of data lies within 1σ of the mean. Review Chapter 5 in
Stats in Your World textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 1 of 26
,Introduction to Statistics - Theorem 2025/12/01, 21:14
2. What percent of cars have a fuel efficiency greater than 1σ above the mean?
A. 50%
B. 16%
C. 68%
D. 32%
Correct Answer: B
Apply the 68-95-99.7 Rule. By definition, 68% of data lies within 1σ of the mean. To find 1σ above the
mean subtract 68% from 100% and divide by 2; (100 – 68)/2 = 16%. Review Chapter 5 in Stats in Your
World textbook for more information.
3. What percent of cars have a fuel efficiency less than 2σ below the mean?
A. 2.5%
B. 5%
C. 95%
D. 99.7%
Correct Answer: A
Apply the 68-95-99.7 Rule. 95% of data is within2σ of the mean. That leaves 5% outside. Half of that is in
one tail; (100 – 5)/2 = 2.5%. Review Chapter 5 in Stats in Your World textbook for more information.
4. What percent of cars have a fuel efficiency between 1σ above the mean and 2σ above the mean?
A. 34%
B. 27%
C. 13.5%
D. 81.5%
Correct Answer: C
Apply the 68-95-99.7 Rule. 47.5% of data lie 2σ above the mean, while 34% lie 1σ above the mean.
Subtract to find the percent in between; (47.5 – 34) = 13.5%. Review Chapter 5 in Stats in Your World
textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 2 of 26
, Introduction to Statistics - Theorem 2025/12/01, 21:14
5. Use this information to answer questions 5-9. Suppose a normal model describes the fuel efficiency of cars
currently registered in your state. The mean is 29 MPG, with a standard deviation of 5 mpg.
What is the range of fuel efficiency for cars within 1σ of the mean?
A. 24 mpg – 34 mpg
B. 28 mpg – 30 mpg
C. 29 mpg – 34 mpg
D. −1 mpg – +1 mpg
Correct Answer: A
Apply the 68-95-99.7 Rule. Find the mean ±5 mpg; 29 − 5 and 29 + 5, 24 mpg – 34 mpg. Review
Chapter 5 in Stats in Your World textbook for more information.
6. What percent of all cars get less than 20 mpg?
A. 31.0%
B. 3.6%
C. 5.5%
D. 50%
Correct Answer: B
Find the z-score, z = (y – µ)/σ, (20 – 29)/5 = −1.80. Then the percent which corresponds to that z-score
by using Table Z; 0.0359 ≈ 3.6%. Review Chapter 5 in Stats in Your World textbook for more information.
https://theorem.nebraska.edu/courses/MTHH041055/Unit-2%2Funit-2-evaluation Page 3 of 26
