Exam 2: Lessons 3 & 4
Name________________
Questions 1-4 refer to the following:
The following table classified eighty-two children by age and favorite meals at Mac Donald restaurant.
|
Age (years) |
6 or below |
7 – 12 |
13 – 15 |
Total |
Restaurant |
Hamburger |
6 |
12 |
16 |
34 |
Chicken Nuggets |
9 |
13 |
11 |
33 |
Filet’o’fish |
2 |
5 |
8 |
15 |
Totals |
17 |
30 |
35 |
82 |
Assume a child is randomly selected.
1. Find the probability of being “7-12” years old AND preferring “chicken nuggets”
A. 13/82 B. 28/82 C. 33/82 D. 13/61
2. Find the probability of being “13-15” years old OR preferring “Filet’o’fish”.
A. 8/82 B. 50/82 C. 8/51 D. 42/82
3. Find the probability of “preferring Hamburger” given that the randomly selected child is 13-15 years old.
A. 16/82 B. 16/35 C. 16/34 D. 16/70
4. The events “preferring Hamburger” and “being 13-15 years old” are:
A. Mutually exclusive B. Independent C. Neither A nor B D. Both A & B
5. E and F are two events such P(E) = 0.60, P(E or F) = 0.90 and P(E and F) = 0.50. Find P(F).
A. 0.80 B. 0.30 C. 0.40 D. 0.10
6. The probability that a randomly chosen adult resident of Bayview city owns a boat is 0.16. The probability that a randomly chosen adult rents an apartment is 0.30. The probability that the adult owns a boat given he/she rents an apartment is 0.20.
Find the probability that a randomly chosen adult rents an apartment and owns a boat is:
A. 0.048 B. 0.24 C. 0.10 D. 0.06
7. Possessing a boat and renting an apartment are:
A. independent events
B. mutually exclusive
C. both independent and mutually exclusive
D. neither independent nor mutually exclusive
Questions 8 - 9 refer to the following:
A bag contains 4 red marbles and 5 blue marbles. Two marbles are randomly drawn without replacement.
8. Find the probability of the event “The first marble is red and the second is blue.”
A. 20/81 B. 20/72 C. 4/12 D. 4/9
9. Find the probability that both marbles are red.
A. 16/81 B. 7/81 C. 12/ 72 D. 8/72
10. Approximately 70% of U. S. adults had at least one pet as a child. We randomly survey 60 U. S. adults. We are interested in the number that had at least one pet as a child. The probability that at least 3 adults had at least one pet as a child means:
A. P(X=0)+P(X=1)+P(X=2)
B. P(X=0)+P(X=1)+P(X=2)+P(X=3)
C. P(X=4)+P(X=5)+P(X=6)+ ... + P(X = 60)
D. P(X=3)+P(X=4)+P(X=5)+ ... + P(X = 60)
Questions 11 & 12 refer to the following:
A plumber has determined the possible number of house calls to be made each day, and their related probabilities:
x =# house calls |
P ( x ) |
0 |
0.10 |
1 |
0.40 |
2 |
0.25 |
3 |
0.15 |
4 |
0.10 |
11. What is the probability that he makes at least 1, but no more than 3 house calls in a day?
A. 0.65 B. 0.80 C. 0.50 D. 0.40
12. If the plumber charges a flat fee of $ 40 for a house call, the expected daily income is:
A. $ 70 B. $ 175 C. $ 400 D. $ 1. 75
13. If X ~ B ( 40 , 0.2 ) , then P ( X > 11 ) =
A. 0.0432 B. 0.0001 C. 0.0875 D. 0.1608
14. The Fizz–Full Soda Company knows that 4% of the bottles of soda it produces are filled with less soda than required. If one purchases 10 bottles at random, the probability that at most 2 of these bottles will have less soda than required is:
A. 0.0519 B. 0.9938 C. 0.9418 D. 0.0080
Questions 15 – 16 refer to the following:
Assume the statistics final is a multiple-choice exam with 50 questions, each question having 5 choices, only one of which is correct. Assume you answer all questions at random (guessing).
15. The expected number of questions you would get correct would be:
A. 5 B. 10 C. 40 D. 45
16. Based upon numerical calculations, would you be surprised if a person got exactly half of the questions correct?
A. yes, because it is impossible B. yes, because the probability is almost 0
C. no, because the probability is 0.50 D. no, because it is the most likely probability
17. If sampling without replacement occurs, do the picks follow the Binomial Distribution?
A. Yes, because each pick is independent from the others.
B. No, because the probability of success on each pick changes.
C. Yes, if we are counting the number of successes.
D. No, because we may not have any successes.
18. Ninety-four percent of California community college transfers feel that their community college adequately prepared them to handle upper-division coursework at their transfer university. We randomly survey 14 California community college transfers. We are interested in the number that feel that their community college adequately prepared them to handle upper division coursework at their transfer university. List the values that X, the Random Variable, may take on.
A. 1, 2, 3, ..., 14 B. 1, 2, 3, ..., 94 C. 0, 1, 2, ..., 14 D. 0, 1, 2, ..., 94
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