Download Test 3A Fall 2016 - Faculty Web Pages

Test 3A
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Solve the problem.
1) An archer is able to hit the bullʹs eye 71% of the time. If she shoots 17 arrows, what is the
standard deviation of the number of bullʹs-eyes that she gets? Assume the shots are independent
of each other.
A) 1.87
B) 4.93
C) 3.5003
D) 8.5
E) 12.07
2) An archer is able to hit the bullʹs eye 48% of the time. If she shoots 25 arrows, how many
1)
2)
bullʹs-eyes do you expect her to get? Assume the shots are independent of each other.
A) 6.24
B) 12.5
C) 2.5
D) 13
E) 12
3) Let A and B be events with P(A) = 0.4, P(B) = 0.9, and P(A and B) = 0.32. Are A and B
mutually exclusive?
A) No
B) Yes
3)
4) Let A and B be events with P(A) = 0.7, P(B) = 0.5, and P(B|A) = 0.4. Find P(A and B).
A) 0.35
B) 0.28
C) 0.2
D) 0.57
4)
Find the probability of the outcome described.
5) A tennis player makes a successful first serve 59% of the time. If she serves 6 times, what is the
probability that she gets no more than 3 first serves in? Assume that each serve is independent of
the others.
A) 0.5236
B) 0.8067
C) 0.2831
D) 0.1933
E) 0.4764
1
5)
Find the indicated probability.
6) The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
10
37
92
44
183
9
32
92
45
178
58
158
317
188
721
Find the probability that the person was a secretary or retired before the age of 61.
A) 0.404
B) 0.092
C) 0.546
D) 0.306
E) 0.455
7) You are dealt a hand of three cards, one at a time. Find the probability that you have at least one
queen.
A) 0.068
B) 0.213
C) 0.783
D) 0.204
6)
7)
E) 0.217
8) An archer is able to hit the bullʹs-eye 55% of the time. If she shoots 8 arrows, what is the
8)
probability that she gets exactly 4 bullʹs-eyes? Assume each shot is independent of the others.
A) 0.0038
B) 0.1719
C) 0.7373
D) 0.0915
E) 0.2627
9) You are dealt a hand of three cards, one at a time. Find the probability that your cards are all
diamonds.
A) 0.705
B) 0.750
C) 0.231
D) 0.016
9)
E) 0.013
10) A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and
10)
19 of the men have high blood pressure. If one of the volunteers is selected at random find the
probability that the person has high blood pressure given that it is a woman.
A) 0.222
B) 0.114
C) 0.234
D) 0.513
E) 0.486
11) An IRS auditor randomly selects 3 tax returns from 54 returns of which 10 contain errors. What is
the probability that she selects none of those containing errors?
A) 0.534
B) 0.466
C) 0.005
D) 0.006
2
E) 0.541
11)
12) An investor is considering a $15,000 investment in a start-up company. She estimates
that she has probability 0.15 of a $5000 loss, probability 0.15 of a $10,000 loss,
probability 0.15 of a $30,000 profit, and probability 0.55 of breaking even (a profit of
$0). What is the expected value of the profit?
A) $6750
B) $10,500
C) $5000
D) $2250
12)
13) Let A, B and C be independent events with P(A) = 0.6, P(B) = 0.3, and P(C) = 0.2. Find
P(A and B and C).
A) 0.18
B) 0.033
C) 0.9
D) 0.036
13)
Find the expected value of the random variable.
14) A couple plans to have children until they get a boy, but they agree that they will not have more
than four children even if all are girls. Find the expected number of children they will have.
Assume that boys and girls are equally likely. Round your answer to three decimal places.
A) 2.500
B) 1.750
C) 1.875
D) 1.938
E) 1.625
Create a probability model for the random variable.
15) You have arranged to go camping for two days in March. You believe that the probability that it
will rain on the first day is 0.3. If it rains on the first day, the probability that it also rains on the
second day is 0.8. If it doesnʹt rain on the first day, the probability that it rains on the second day
is 0.3.
Let the random variable X be the number of rainy days during your camping trip. Find the
probability model for X.
0
1
2
A) Rainy days
P(Rainy days) 0.49 0.21 0.24
0
1
2
B) Rainy days
P(Rainy days) 0.14 0.62 0.24
0
1
2
C) Rainy days
P(Rainy days) 0.49 0.27 0.24
0
1
2
D) Rainy days
P(Rainy days) 0.49 0.42 0.09
0
1
2
E) Rainy days
P(Rainy days) 0.49 0.06 0.24
16) A fair die is rolled two times. What is the probability that both rolls are 3?
A) 0.167
B) 0.0046
C) 0.083
D) 0.028
3
14)
15)
16)
17) Compute the mean of the random variable with the given discrete probability distribution 17)
x
0
10
25
30
A) 18
P(x)
0.2
0.2
0.4
0.2
B) 126.0
C) 11.2
D) 16.25
18) Fill in the missing value so that the following table represents a probability distribution.
18)
x
-2
-1 0 1
P(x) 0.05 0.47 ? 0.32
A) 0.07
B) 0.25
C) 0.16
D) 0.02
19) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the
slips are placed into a hat. If the slips are drawn randomly without replacement, what is
the probability that "A" is drawn first and "B" is drawn second?
A) 0.039
B) 0.024
C) 0.033
D) 0.028
4
19)
Answer Key
Testname: TEST 3A FALL 2016
1) A
2) E
3) A
4) B
5) E
6) E
7) E
8) E
9) E
10) A
11) A
12) D
13) D
14) C
15) C
16) D
17) A
18) C
19) C
5