Math 113 Fall 2007 Final

1. A light bulb manufacturer wants to know the mean burning time of the light bulbs it

produces. A random sample of 2000 bulbs is taken, each bulb is used until it burns out and

the sample mean burning time is found. The company concluded that a 95% confidence

interval for the true mean burning time of all its light bulbs is 2035 ± 24.6 hours.

If the company wishes to decrease the width of the confidence interval, it may do so by

A) decreasing the sample size to less than 2000 bulbs.

B) decreasing the confidence level to less than 95%.

C) increasing the mean burning time of its light bulbs.

D) increasing the confidence level to more than 95%.

2. Suppose an architect needs to design an intercom system for a large office building. The

technique most likely to be useful in solving this problem is:

A) finding an Euler circuit on a graph.

B) applying the nearest-neighbor algorithm for the traveling salesman problem.

C) applying Kruskal's algorithm for finding a minimum-cost spanning tree for a graph.

D) finding the chromatic number of a graph.

3. Find the chromatic number of the graph below:

A) 9 B) 6 C) 3 D) 2

4. Exactly one of Terry, Chris and Kim will attend a party. The probability Terry attends is 0.31

and the probability Chris attends is 0.5. What is the probability that Kim attends?

A) 0.33 B) 0.5 C) 0.81 D) 0.19

5. There are seven blue and six black socks in a drawer. One is pulled out at random. Find the

probability that it is black.

A) 6/13 B) 6/7 C) 1/2 D) 1/6

6. You have $1000 that you invest at 5% simple interest. How long will it take for your balance

to reach $1250?

A) 10 years B) 7 years C) 5 years D) 4 years

7. Use the Venn diagram method to decode the received word 1011001.

A) 1011 B) 1010 C) 1001 D) 0010

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8. Which of the following describes a Hamiltonian circuit for the graph below?

A) ABCDEJHIGF B) AEDCBGIHJFA

C) ABCDEAFGHIJFA D) ABCDEAFGBGIDIHCHJEJFA

9. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the

nearest-neighbor algorithm, starting at A?

A) 215 B) 220 C) 235 D) 295

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10. A group of twenty-two young people must decide whether to go to the beach (B), the

mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the

table below. Which choice wins using the Borda count?

Number of Voters

10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B

A) M B) B

C) Z D) No winner is determined.

11. The scores of students on a standardized test are normally distributed with a mean of 300

and a standard deviation of 40. What is the probability that a randomly chosen student scores

below 273.2 on the test?

A) 0.025 B) 0.25 C) 0.165 D) 0.125

12. Suppose a US Postal Service money order is numbered x2639203210 where the first digit is

obliterated. What is the missing digit?

A) 4 B) 5

C) 8 D) The missing digit can't be determined.

13. Below are the number of errors made by a typist on various pages of typing. Find the

third quartile for the number of errors.

14, 6, 12, 19, 2, 35, 5, 4, 3, 7, 5, 8

A) 4.5 B) 5 C) 13 D) 15.5

14. A sample of 50 people at a local fast-food restaurant found 15 in favor of new fat-free menu

items. In this example, the sample proportion is

A) 15%. B) 25%. C) 30%. D) 50%.

15. Determine the check digit that should be appended to the ISBN 0-7167-6531.

A) 1 B) 4 C) 6 D) 8

16. A local cafeteria offers a choice of 5 meats, 6 vegetables, and 3 salads. A complete dinner

includes 1 meat, 1 vegetable, and 1 salad. How many different dinners can be created?

A) 14 B) 45 C) 90 D) 120

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17. The mean shelf life of a battery produced by one major company is known to be 3.5 years

with a standard deviation of 0.75 years. A random sample of 25 batteries is selected and the

mean life determined. What is the standard deviation of the sampling distribution for the

mean life?

A) 0.15 years B) 0.03 years C) 0.173 years D) 0.035 years

18. To determine the proportion of students at a university who favor the construction of a

parking garage, a random sample of people chosen from current enrollment lists is surveyed

and it is found that 43% favor the garage. The actual proportion of the student body who

favor the garage is 40%. In this example, 43% is a

A) population. B) parameter. C) sample. D) statistic.

19. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the

sorted-edges algorithm?

A) 40 B) 58 C) 60 D) 66

20. In order to eulerize the graph below, give the fewest number of edges that need to be

added or duplicated?

A) 4 B) 6 C) 10 D) 12

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21. You wish to survey the students at your college to determine their feelings about the quality

of services in the Student Center. Which of the following sampling designs is best for

avoiding bias?

A) Place an ad in the student newspaper asking all readers to mail in their opinions.

B) Obtain a list of student names from the registrar and select 250 names to contact.

C) Air an announcement on the campus radio station asking all listeners to phone in their

opinions.

D) Survey every tenth student who enters the Student Center.

22. How many votes are needed for a majority winner if there are 120 voters?

A) 60 B) 61 C) 119 D) 120

23. In order to determine the mean weight of bags of chips filled by its packing machines, a

company inspects 50 bags per day and weighs them. In this example, the population is

A) the 50 bags inspected each day.

B) all potato chips produced by the company.

C) all bags of chips produced by the company.

D) the weight of the 50 bags inspected.

24. In which of the diagrams below do the wiggled edges represent spanning trees?

A) I only B) II only C) I and II both D) Neither I or II

25. The shelf life of a battery produced by one major company is known to be normally

distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the

upper quartile of battery shelf life, to two decimal places?

A) 4.00 years B) 4.17 years C) 4.25 years D) 5.50 years

26. Which of the following statements about a connected graph is always true?

A) Every pair of vertices is joined by a single edge.

B) A path of edges exists between any two vertices of the graph.

C) There are an even number of vertices on the graph.

D) There are an even number of edges on the graph.

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27. Given the histogram of waiting times for patients at a health clinic, which statement is true?

A) The histogram is roughly symmetric.

B) The class from 50 to 59 minutes represents 10 outliers.

C) There is a gap in the histogram.

D) The histogram is skewed to the right.

28. What is the valence of vertex A in the graph below?

A) 3 B) 5 C) 7 D) 11

29. Below are the ages of 15 students in a college class. Find the mean age.

27, 50, 33, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28

A) 34 B) 31 C) 41.3 D) 20.6

30. Let C be the code {101010, 010101, 111111, 000000}. What is the weight of this code?

A) 0 B) 1 C) 3 D) 6

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31. Your fly fishing club is attempting to decide where to go for the next day trip. The choices

are Alder River (A), Boulder Pond (B), or Collie Creek (C). The preference rankings of the

members are shown below.

Number of members

6

12

15

11

First choice

A

C

B

A

Second choice

B

B

A

C

Third choice

C

A

C

B

Which location will be chosen if the Hare system is used?

A) Alder River B) Boulder Pond

C) Collie Creek D) No winner can be chosen.

32. Consider a loan at 5% interest, compounded monthly. Which is true?

A) The APY is 5%, the APR is higher. B) The APY is 5%, the APR is lower.

C) The APR is 5%, the APY is higher. D) The APR is 5%, the APY is lower.

33. Dave borrowed $2000 from her parents, agreeing to pay them back when she graduated

from college in five years. If he paid interest compounded quarterly at 5%, how much would

she owe at the end of the five years?

A) $2100 B) $2564 C) $3006 D) $3162

34. Use the Venn diagram method to determine the code word of the message 1010.

A) 1010110 B) 1010111 C) 1010001 D) 1010011

35. Use Kruskal's algorithm for minimum-cost spanning trees on the graph below. The cost

of the tree found is:

A) 47 B) 25 C) 22 D) 15

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Math 113 Final Exam – Fall 2007 Answers

1.

B

8.

B

10.

A

17.

A

21.

B

27.

C

31.

B

2.

C

9.

B

11.

B

18.

D

22.

B

28.

B

32.

C

3.

C

12.

C

19.

D

23.

C

29.

C

33.

B

4.

D

13

C

20.

B

24.

B

30.

C

34.

C

5.

A

14.

C

25.

A

35.

C

6.

C

15.

B

26.

B

7.

B

16.

C

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