Download EXAM 2 - Math TAMU

EXAM 3
7.1-7.6, 8.1-8.3
MATH 141 Business Mathematics I
Fall 2006 Version A
Nite
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
You have 75 minutes to complete the exam.

You must show appropriate, legible work to receive credit. Include all
intermediate steps and functions you use on your calculator.

Check to make sure there are 5 pages, besides the cover page, before you begin.

All answers must be exact decimals or reduced fractions unless specified otherwise.
Be sure your answer is clearly legible. If there is any doubt, it is wrong.

Each standard deck of 52 cards has 4 suits: Hearts, Diamonds, Clubs, and
Spades. Within each suit there are 13 cards, labeled Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10,
Jack, Queen, and King. The face cards are Jacks, Queens, and Kings.

SCHOLASTIC DISHONESTY WILL NOT BE TOLERATED.
GOOD LUCK!!
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
Circle the correct classification of the following random variables. Find the values
the random variable may have. (3 pts each)
1. X = the number of times a student draws without replacement to get a blue marble from
a box containing 5 red and 3 blue marbles.
finite discrete
infinite discrete
continuous
Values of X: _____________________
2. Y = the number of times a coin is tossed to get a tail 6 times.
finite discrete
infinite discrete
continuous
Values of X: _____________________
3. Z = the distance a vacationer travels.
finite discrete
infinite discrete
continuous
Values of X: _____________________
4. U = the number of hours a day a parent works.
finite discrete
infinite discrete
continuous
Values of X: _____________________
The random variable X may only assume the values 2, 3, 4, 5, and 6. Complete the
given histogram, and find the following. If necessary, round answers to 3 decimal
places. (2 pts each)
5. P(X = 4) = ____________
6. P(X > 2) = ____________
0.7
0.6
7. Mode of X = ____________
0.5
8. Median X = ____________
9. Var(X) = ____________
10. x = ______________
P(X=x)
0.4
0.3
0.2
0.1
x
0 1 2 3 4 5 6 7 8 9
11. Write the non-uniform sample space formed when picking a letter at random from the
word BUSINESS. (4 pts)
12. E and F are mutually exclusive events and P(E) = 0.6 and P(F) = 0.35.
Find P(E  FC). (4 pts)
13. The uniform sample space for an experiment is S = {0, 1, 2, 3}. How many events
contain an odd integer? (4 pts)
14. If the probability that Cara passes her math test is
4
, what are the odds that she fails
5
her math test? (4 pts)
An experiment consists of rolling a fair six-sided die (numbered 1-6) and a fair fivesided die (numbered 1-5). Answer the following four questions about the
experiment.
15. How many events are associated with this experiment? (2 pts)
16. How many of the events associated with this experiment are simple events? (2 pts)
17. Let E be the event that the six-sided die shows an odd number and let F be the event
that the sum of the dice is either 7 or 8. Find P(E F). (4 pts)
18. For the events E and F in problem #17, find P(E | F). (3 pts)
19. Are the events E and F in problem #17 independent events? Justify your answer.
(3 pts)
The letters of the word SUPERCALIFRAGILISTIC are placed on slips of paper and placed
into a box. You randomly select 7 pieces of paper from the bag.
20. What is the probability that you select all of the I’s? (4 pts)
21. What is the probability that you select at least 6 consonants? (4 pts)
Given the following tree diagram and that G is the event that a student is enrolled in
a geography class and H is the event that a student is enrolled in a history class,
answer the following four questions. (3 pts each)
H
0.7
G
HC
0.45
H
GC
0.4
HC
22. What is the probability that a randomly selected student is enrolled in a geography
class and a history class?
23. What is the probability that a randomly selected geography student is not enrolled in a
history class?
24. What is the probability that a randomly selected student is enrolled in a history class?
25. What is the probability that a randomly selected history student is enrolled in a
geography class?
26. Draw a tree diagram to represent the following problem. Clearly define your events
and indicate the appropriate probabilities on each branch. (8 pts)
Three balls are sequentially selected at random without replacement from an urn
containing four black balls and five white balls.
At the county fair you pay $3.00 to play in the following game:
A spinner device is numbered from 1 to 5, and each of the numbers is as
likely to come up as any other. You bet and additional $1 on a given
number. If the pointer comes to rest on your chosen number, you win $4
(and get the bet back); otherwise, you lose the $1 bet.
27. Find the probability distribution of your net winnings. (4 pts)
28. What are your expected net winnings? (2 pts)
29. If the winnings stay the same, what should be the price for the game to make it a fair
game? (2 pts)
The following table gives the scores of 100 students in a mathematics examination:
Scores
90-99
80-89
70-79
60-69
50-59
40-49
Number of
Students
8
19
27
28
11
7
Use the midpoint for each score group in your calculations. For example, the use the
midpoint of 44.5 for the scores 40-49.
Find the following measures of central tendency and variation for the data given above.
(2 pts each)
30. Mean
31. Median
32. Mode
33. Standard Deviation
34. Variance