Download MATH 102 Final Exam Practice Fall 2012 Use the information below

MATH 102
Final Exam Practice
Fall 2012
Use the information below to answer questions 1-4.
Let
U = {Sun., Mon., Tue., Wed., Thur., Fri., Sat.}
B = {Sat., Sun.}
1. Find A  C.
2. Find the complement of C.
3. Find A  C.
4. Find (A  C)  B.
A = {Mon., Wed., Fri., Sat.}
C = {Tue., Wed., Thur.}
Use the diagram below to answer questions 5 and 6.
5. Give the numbered regions that represent A  B  .
6. Give the numbered regions that represent C  ( A  B) .
Use the information below to answer questions 7-9.
An activities director for a summer camp has surveyed 300 teenagers. Of the 300 teens,
125 like swimming
140 like dancing
75 like singing
60 like swimming and dancing
25 like swimming and singing
10 like dancing and singing
5 like all three activities
7. How many teenagers like singing but not dancing?
8. How many teenagers like swimming only?
9. How many teenagers do not like any of the three activities?
10. Write the negation of “Some 2 year olds are bad.”
11. Negate: “If Ivan studies, then he will succeed.”
Use truth tables to answer questions 12 and 13.
12. Is ~ p  ~ q a tautology?
13. Is (p  q)  ~ p a tautology?
Use the statement below to answer questions14-16.
“If Marcus drives fast, then he may have an accident.”
14. Write the converse of the statement.
15. Write the inverse of the statement.
16. Write the contrapositive of the statement.
Use Euler circles to find the validity of the arguments in questions 17 and 18.
17. Some mathematics courses have algebra.
Geometry is a mathematics course.
Therefore, geometry has no algebra.
18. All prime numbers are odd.
2 is a prime number.
Therefore, 2 is an odd number.
Write a valid conclusion for questions 19−21.
19. I will go sailing or I will play cards.
I do not play cards.
Therefore, ________________________ .
20. If I study, then I will learn.
If I learn, then I will perform.
Therefore, ________________________ .
21. Charlene reviews for her test, or Wayne chats on his cell phone.
Wayne does not chat on his cell phone.
Therefore, ________________________ .
22. A restaurant offers a choice of 2 salads, 3 entrees, and 4 desserts. How many different meals
consisting of a salad, an entree, and a dessert are possible?
23. Two cards are drawn in succession without replacement from a standard deck of 52. In how
many ways could this be a queen and a jack in that order?
24. How many different sums of money can be made from a set of coins consisting of a penny, a
nickel, a dime, a quarter, a half-dollar, and a silver dollar if exactly 2 coins are used for each
sum?
25. Three cards are drawn in succession without replacement from a set of 10 cards. How many
different sets of 4 cards are possible?
26. How many different arrangements can you make with the letters in the word statistics?
Use the information below to answer questions 27 and 28.
A box contains 9 balls numbered 1 to 9. A ball is taken at random from the box.
27. Find the probability that the ball has an odd number.
28. Find the probability that the ball does not have an odd number.
29. Two cards are drawn at random in succession, without replacement, from a standard deck of
52. Find the probability that both cards are red.
30. An urn contains 6 white, 4 blue, and 2 green balls. Find the probability of obtaining a white
or blue ball in a single draw.
31. A box has 3 defective video tapes and 7 good video tapes. If 2 tapes are selected at random,
what is the probability that they are both good?
32. A card is selected at random from a deck of 52 cards. What are the odds in favor of the card
being a king?
Use the data below to answer questions 33 and 34.
The following values represent the number of cigarettes persons smoke per day:
10
13
8
12
6
15
14
15
22
5
13
11
17
16
19
11
11
9
18
14
33. Make a frequency distribution using the groups 5–8, 9–12, 13–16, 17–20, and 21–24.
34. Draw the corresponding histogram.
Use the data below to answer questions 35-39.
The following values are gas prices from 8 local gas stations in September 2006:
$1.98
$2.05
$2.29
$2.17
$2.05
$2.14
$2.05
$2.01
35. Find the mean gas price.
36. Find the median gas price.
37. Find the modal gas price.
38. Find the range of gas prices.
39. Find the standard deviation.
Use the information below to answer questions 40 and 41.
A teacher finds that the mean score of his class is 72 with a standard deviation of 8. (Use the
table in the back of the book, if needed.)
40. Find the z-score corresponding to 50.
41. Find the probability that a student will have a score between 72 and 80.