Review Problems For Mid-Term 2 , Fall 2012 (STA-120)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated complement.
1) Find P(A), given that P(A) = 0.732.
A) 0.268
B) 1.366
1)
C) 1.732
D) 0
Find the indicated probability.
2) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
433
50
66
34
583
Women
408
31
70
35
544
Total
841
81
136
69
1127
If one of the 1127 people is randomly selected, find the probability that the person is a man or a
heavy smoker.
A) 0.493
B) 0.548
C) 0.579
D) 0.518
2)
3) A study of consumer smoking habits includes 183 people in the 18-22 age bracket (59 of whom
smoke), 140 people in the 23-30 age bracket (34 of whom smoke), and 99 people in the 31-40 age
bracket (22 of whom smoke). If one person is randomly selected from this sample, find the
probability of getting someone who is age 18-22 or does not smoke.
A) 0.867
B) 1.161
C) 0.678
D) 0.294
3)
4) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).
13
2
4
A)
B)
C) 8
D)
2
13
13
4)
5) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and
30% are defective. If three of the products are randomly selected, find the probability that all of
them are acceptable.
A) 0.027
B) 2.1
C) 0.343
D) 0.429
5)
6) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men
305
42
31
378
Women
442
34
30
506
Total
747
76
61
884
6)
If two different people are randomly selected from the 884 subjects, find the probability that they
are both women. Round to four decimal places.
A) 0.000003906
B) 0.2500
C) 0.3276
D) 0.3274
Evaluate the expression.
7) 10P5
A) 2
7)
B) 5
C) 30,240
D) 252
Solve the problem.
8) The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles. If each
book selected must have a different title, how many possible selections are there?
A) 4096
B) 3360
C) 48
D) 560
8)
9) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to
choose from?
A) 20,160
B) 40,320
C) 720
D) 48
Find the mean of the given probability distribution.
10) In a certain town, 40% of adults have a college degree. The accompanying table describes the
probability distribution for the number of adults (among 4 randomly selected adults) who have a
college degree.
x
P(x)
0 0.1296
1 0.3456
2 0.3456
3 0.1536
4 0.0256
A) μ = 1.50
B) μ = 1.73
C) μ = 1.60
D) μ = 2.00
Provide an appropriate response. Round to the nearest hundredth.
11) Find the standard deviation for the given probability distribution.
x P(x)
0 0.12
1 0.07
2 0.21
3 0.30
4 0.30
A) σ = 2.90
B) σ = 1.70
C) σ = 1.35
9)
10)
11)
D) σ = 1.30
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The
probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table.
Probabilities of Girls
x(girls) P(x) x(girls) P(x) x(girls) P(x)
0
0.000
5
0.122
10
0.061
1
0.001
6
0.183
11
0.022
2
0.006
7
0.209
12
0.006
3
0.022
8
0.183
13
0.001
4
0.061
9
0.122
14
0.000
12) Find the probability of selecting 9 or more girls.
A) 0.122
B) 0.001
12)
C) 0.061
D) 0.212
Provide an appropriate response.
13) A contractor is considering a sale that promises a profit of $33,000 with a probability of 0.7 or a loss
(due to bad weather, strikes, and such) of $16,000 with a probability of 0.3. What is the expected
profit?
A) $18,300
B) $34,300
C) $17,000
D) $23,100
13)
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal
places.
14) n = 30, x = 12, p = 0.20
14)
A) 0.006
B) 0.108
C) 0.003
D) 0.014
Find the indicated probability. Round to three decimal places.
15) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are
selected at random from the physics majors, that is the probability that no more than 6 belong to an
ethnic minority?
A) 0.913
B) 0.055
C) 0.985
D) 0.982
Find the indicated probability.
16) An archer is able to hit the bull's-eye 53% of the time. If she shoots 10 arrows, what is the
probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
A) 0.0789
B) 0.000851
C) 0.179
D) 0.0905
Solve the problem.
17) The probability that a person has immunity to a particular disease is 0.8. Find the mean number
who have immunity in samples of size 17.
A) 0.8
B) 8.5
C) 13.6
D) 3.4
15)
16)
17)
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
18) n = 639; p = 0.7
18)
A) σ = 9.17
B) σ = 11.58
C) σ = 15.70
D) σ = 14.85
Solve the problem.
19) On a multiple choice test with 19 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 9.5
B) 6.3
C) 4.8
D) 14.3
Use the Poisson Distribution to find the indicated probability.
20) A mountain search and rescue team receives a mean of 0.44 calls per day. Find the probability that
on a randomly selected day, they will receive fewer than two calls.
A) 0.9274
B) 0.0623
C) 0.2834
D) 0.0726
19)
20)
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
21)
21)
-1.82
A) 0.9656
z
1.82
B) -0.0344
C) 0.0344
D) 0.4656
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
22) Shaded area is 0.0694.
22)
z
A) 1.39
B) 1.45
C) 1.48
D) 1.26
23) Shaded area is 0.0901.
23)
z
A) -1.26
B) -1.39
If z is a standard normal variable, find the probability.
24) The probability that z is less than 1.13
A) 0.8485
B) 0.1292
C) -1.45
D) -1.34
C) 0.8708
D) 0.8907
24)
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some
give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the
frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
25) If 7% of the thermometers are rejected because they have readings that are too high, but all other
25)
thermometers are acceptable, find the temperature that separates the rejected thermometers from
the others.
A) 1.45°
B) 1.48°
C) 1.26°
D) 1.39°
Assume that X has a normal distribution, and find the indicated probability.
26) The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Find the probability that X is greater than 15.2.
A) 0.5000
B) 0.9998
C) 1.0000
27) The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Find the probability that X is between 14.3 and 16.1.
A) 0.8413
B) 0.3413
C) 0.1587
26)
D) 0.0003
27)
D) 0.6826
Find the indicated probability.
28) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a
standard deviation of $45. What is the probability that a randomly selected teacher earns more than
$525 a week?
A) 0.2823
B) 0.2177
C) 0.7823
D) 0.1003
Solve the problem.
29) The weights of the fish in a certain lake are normally distributed with a mean of 19 lb and a
standard deviation of 6. If 4 fish are randomly selected, what is the probability that the mean
weight will be between 16.6 and 22.6 lb?
A) 0.0968
B) 0.6730
C) 0.4032
D) 0.3270
30) A final exam in STA-120 has a mean of 73 with standard deviation 7.8. If 24 students are randomly
selected, find the probability that the mean of their test scores is greater than 78.
A) 0.8962
B) 0.0103
C) 0.0008
D) 0.0036
28)
29)
30)
Answer Key
Testname: STA120RT2F12
1) A
2) B
3) A
4) B
5) C
6) D
7) C
8) D
9) A
10) C
11) D
12) D
13) A
14) A
15) D
16) C
17) C
18) B
19) C
20) A
21) A
22) C
23) D
24) C
25) B
26) A
27) D
28) B
29) B
30) C