Project 3
Evaluation 33
Introduction to Statistics (MTHH 041 055)
Be sure to include ALL pages of this project (including the directions and the assignment) when you send the project to your teacher for grading. Don’t forget to put your name and I.D. number at the top of this page!
This project will count for 11% of your overall grade for this course. Be sure to read all the instructions and assemble all the necessary materials before you begin. You will need to print this document and complete it on paper. Feel free to attach extra pages if you need them.
To earn full credit, you must justify your solutions by showing your work.
When you have completed this project, you may submit it electronically through the online course management system by scanning the pages into either .pdf (Portable Document Format), or .doc (Microsoft Word document) format. If you scan your project as images, embed them in a Word document in .gif image format. Using .gif images that are smaller than 8 x 10 inches, or 600 x 800 pixels, will help ensure that the project is small enough to upload. Make sure your pages are legible before you upload them.** Check the instructions in the online course for more information.

You will need to justify your work in order to receive full credit on these problems. Double-check your work before moving forward.
Part A: Questions 1 – 8
1. Give a definition AND example in your own words for each of the concepts. (20 pts)
a. Law of Large Numbers

b. The non-existent law of averages

c. Fundamental Counting Principle (for “and” & “or”)

d. Permutation

e. Combination
2. A raffle has four prizes. Explain why the chance of winning a prize is not 1 out of 4. (2 pts)

3. Including you, there are 10 boys and 18 girls in your chemistry class. (4 pts)
a. How many ways can one boy and one girl be chosen to run an errand for the teacher?

b. How many ways can one boy or one girl be chosen?

4. There are 12 suspects of a crime. How many ways can 4 of them be included in a lineup? (2 pts)

5. A committee of five members is to be randomly selected from a group of eight freshmen and six sophomores. (5 pts)
a. How many different committees of three freshmen and two sophomores can be chosen?

b. What is the probability that Jake, a freshmen, is randomly chosen for a committee?

6. Thinking about 5-card poker hands… (8 pts)
a. How many hands are possible?

b. How many hands with exactly 3 aces are possible?

c. How many hands with exactly 1 or 2 aces are possible?

7. Passwords for a cell phone use two letters followed by two digits followed by a special symbol ( #, $, %, or &), as in AW52$. Any can be repeated. (5 pts)
a. How many passwords are possible?

b. What’s the probability that a password generated randomly in the above format will contain one’s first and last name initials, in order?

8. Seven African American, 5 Asian, 6 Hispanic, and 4 White students are finalists to participate in a summer enrichment camp. From these students, 6 winners will be selected randomly. What’s the probability there will be no Hispanics among the winners? If this occurs, will you suspect foul play? Explain. (5 pts)

Part B: Questions 9 – 12
9. 36% of the patients of a medical office are male. Of those males, 85% say they are satisfied with the care they are receiving. What is the probability that a patient selected at random from this office’s patients is a male who is satisfied with the care he is receiving? (2 pts)

10. When asked about their support of two bills, 35% of congressmen supported Bill A, 62% supported Bill B and 14% supported both. (8 pts)
a.Draw a Venn diagram.

b.Find the probability that a congressman selected at random…
i.supports Bill A or Bill B.

ii.supports Bill B but not Bill A.

iii.supports neither Bill A nor Bill B.

11. While looking over the test scores for one of her classes, a teacher tabulated that of the 24 students, 17 students completed all the homework for the unit, 18 students passed the unit test, and 15 students completed all the unit homework and passed the test. (16 pts)
a.Organize this information in a two way table.

b.If one student is selected randomly, find the probability that…
i.the student passed the test.

ii.the student did not complete the homework.

iii.the student completed the homework and passed the test.

iv.the student passed the test given s/he completed the homework.

v.the student completed the homework if s/he passed the test.

c.In this example, is test success independent of homework completion? Explain.

12. There are 23 Halloween candies in a jar. 14 are black and 9 are orange in color. Ramon randomly picks two Halloween candies, one at time. (13 pts)
a.Draw a tree diagram showing the probabilities of the colors Ramon could pick.

b.Ramon has picked a black candy. What is the probability that his second pick is an orange candy.

c.Find the probability that Ramon…
i.picks an orange candy then a black candy.

ii.picks a black candy given he has already picked an orange candy.

iii.picks two different colored candies.

iv.picks no orange candies.

Part C: Questions 13 – 15
13. According to infoplease, 19.1% of the luxury cars manufactured in 2003 were silver. A large car dealership typically sells 45 luxury cars a month. (11 pts)
a.Explain why the question of whether luxury cars sold that are silver can be considered Bernoulli trials.

b.What is the probability that the fifth luxury car sold next month will be the first silver one?

c.What is the probability that exactly ten of the 45 luxury cars sold are silver?

d.What is the probability that at least ten of 45 luxury cars sold are silver?

e.Find the mean and standard deviation of the number of silver luxury cars sold at this dealership each month.

mean = _________________ standard deviation = ___________________

14. Safety officials hope a public information campaign will increase the use of seatbelts above the current 70% level. After several months they check the effectiveness of this campaign with a statewide survey of 600 randomly chosen drivers. 440 of those drivers report that they wear a seatbelt. (8 pts)
a.Verify that a Normal model is a good approximation for the binomial model in this situation.

b.Find the mean and standard deviation of the Normal model.

c.Does the survey result convince you that the education/advertising campaign was effective? Explain.

15. Alcohol is claimed to be a factor in 39% of all fatal car accidents in the United States. The town police chief is reviewing a random sample of 55 local car accident records to compare to the national data. How many of the sample records need to show alcohol as a factor to suggest a significant difference exists between the national and local rate of alcohol related car accidents? Explain using standard deviations. (5 pts)

This project can be submitted electronically. Check the Project page in the UNHS online course management system or your enrollment information with your print materials for more detailed instructions.