Illinois State University Mathematics Department

MAT 312: Probability and Statistics for Middle School Teachers

Spring 1999
9:35 - 10:50 am TR STV 350A
Dr. Roger Day (

Problem Set #3
look at possible solutions

This problem set represents approximately 2% of your grade.

Please start each problem set on a new sheet of paper and clearly label your response to each question.

Written responses should be in complete sentences and visual representations should be drawn neatly and accurately.

A value from 0 through 10 will be assigned to your work, based on accuracy, completeness, and clarity of your responses:

10: outstanding--virtually no errors, complete and thoughtful responses

9: sufficient--few if any errors, solid effort

8: adequate--some significant errors, all problems attempted

6: incomplete--many significant errors, some problems not attempted

0: nothing turned in

As on any problem set, you may work in teams of up to three and submit one paper for your team.

A. Car maintenance is not my favorite activity. Even the mundane chore of changing the oil is a pain. I usually wait longer than recommended to change the oil in my car. The owner of a local service station wanted to know whether other drivers had such bad habits, so he conducted a survey of his records to determine the length of time (in months) between customer oil changes. He randomly sampled station records and found the following 15 times (in months) between oil changes:


1. Compute the sample mean and the sample standard deviation for this data.

2. Determine the 5-number summary for this data.

3. Suppose the data value 24 months was incorrectly copied from station records. It should have been 4 months. Which measure of central tendency, the mean or the median, will be most affected by this change? Explain.

B. The table here shows cigarette consumption per adult per year and the number of deaths per 100,000 people per year from coronary heart disease (CHD) for 21 developed countries.

4. Draw a scatter plot of the data, using cigarette consumption on the horizontal axis.

5. Use the median-median line technique to determine a regression line for the data. Follow these steps:

a) Show the scatter plot partitioned into three sets of seven points each.
b) On your scatter plot, identify the median median point in each of the three sections.
c) Calculate and state the slope of the line passing through the first and third median median points.
d) Identify the ordered pair that is the point in the middle section through which the regression line should pass. Describe how you determined this point.
e) Write the equation of this median-median line.

6. Use your median-median regression line equation (question 5e) to determine:

a) the predicted number of deaths from CHD in a country where the adult consumption of cigarettes is 3000 cigarettes per year.

b) the predicted number of cigarettes consumed per year by adults in a country where the CHD mortality rate is 150 deaths per 100,000 people.

7. Describe the meaning of the slope of the median-median line. What does it represent relative to the situation described?

8. Describe the meaning of the vertical-axis intercept of the median-median line. What does it represent relative to the situation described? Is it reasonable and appropriate? Explain.

9. Use your calculator to determine the least-squares regression line for this data.

10. On your scatter plot (or a copy of it), plot the regression lines determined in (5) and (9). Compare the effectiveness of the lines for prediction purposes. Which one is more effective? Justify your response.

C. Counting Problems

Questions 11-13: All automobile license plates in Minnesota have six characters. The characters can be letters of the alphabet (A, B, . . . , Z) or single-digit numbers (0, 1, . . . , 9).

11. If a license plate has four letters followed by two digits, with repetition allowed, how many different license plates are possible?

12. If a license plate again has four letters followed by two digits, this time with repetition not allowed, how many different license plates are possible?

13. If a license plate has three letters followed by three digits, with no repetitions allowed and no use of either the letter O or the digit 0, how many different license plates are possible?

Questions 14-15: From a class of 20 students, a committee of 3 is to be formed to organize a fund raiser.

14. If all 20 students are eligible for committee membership, how many different committees could be formed?

15. If there are 12 women and 8 men in the class, and the committee requires at least one member of each gender, how many different committees could be formed?

Questions 16-21: Use Set I: {d,g,o}, Set II: {c,e,h,i,k,n}, Set III: {a,r,s,t}

16. One letter is to be chosen from Set I or Set II or Set III. How many possible choices exist?

17. A 3-letter set is to be created consisting of one letter from each of Sets I, II, and III. How many such 3-letter sets are possible?

18. How many 6-letter arrangements are possible using the letters in Set II?

19. How many 2-letter sets can be made from the letters in Set III?

20. How many 5-letter arrangements can be made such that the first and last letters are from Set I and the other three letters are from Set III?

21. How many arrangements of the letters in Set II can be made so that no vowels are adjacent to each other?

Questions 22-24: A postal worker entered Complex A of Reeseman Apartment Marketway and approached the row of mail boxes in the hallway. In a slot on each box was a label showing the name of the apartment dweller and a two-digit number for the apartment, as shown below.

J. Hawks Apt 10
M. & M. Sweets Apt 12
U. R. Bigg Apt 14
T. Off Apt 16
S. Teemed Apt 18
Y. R. U. Heer Apt 20

22. How many letters must the postal worker have to assure that at least one of the apartment dwellers would be delivered at least two letters?

23. What is the least number of letters the postal worker must have to assure that at least one of the apartment dwellers will be delivered more letters that his or her apartment number?

24. Suppose that in Building K of the apartment complex there are n apartments, numbered with consecutive even numbers 2 through 2n. How many letters must the letter carrier have to assure that at least one of the apartment dwellers in Building K would be delivered at least m letters?

Question 25: A fast-food chain advertises that it serves hamburgers in more than 1000 ways. The chain offers its burgers with various combinations of mustard, catsup, mayonnaise, Cajun spices, pickles, lettuce, cheese, and type of bun.

25. Is the chain's advertising claim legitimate? Explain.

Assigned: Tuesday 16 March 1999

Due: Tuesday 30 March 1999