# apu math302 quiz 2 done on april 2015

December 9, 2017

Question 1 of 20
1.0/ 1.0 Points
If one tosses a coin enough times, the proportion of
“heads” will approach 0.5. This is an example of:
A.the Central Limit
Theorem
B.subjective
probabilities
C.the Empirical Rule
D.the Law of Large Numbers

Question 2 of 20
1.0/ 1.0 Points
If events A and B are mutually exclusive, then the
probability of both events occurring simultaneously is equal to
A.any value between
0.5 and 1.0
B.1.0
C.0.0
D.0.5

Question 3 of 20
1.0/ 1.0 Points
If two events are independent, what is the probability that
they both occur?
A.0.0
B.0.5
C.1.00
D.Cannot be
determined from the information given

Question 4 of 20
0.0/ 1.0 Points
The number of ways to choose two representatives from a
committee of 13 people is
A.13!
B.156
C.55
D.78

Feedback: This is the combination of 13 objects taken 2 at a
time.
Question 5 of 20
1.0/ 1.0 Points
In a recent study, the following data were obtained in
response to the question, “Do you favor recycling in your neighborhood?”

Yes
No
No Opinion
Males
25
15
10
Females
30
10
10

If a person is
picked at random, what is the probability that the person is either male or has
no opinion regarding recycling?
A.3/5
B.3/10
C.4/5
D.7/10

Part 2 of 6 – 3.0/
5.0 Points

Question 6 of 20
0.0/ 1.0 Points
The following data were obtained from a survey of college
students. The variable X represents the number of non-assigned books read
during the past six months.

x
0
1
2
3
4
5
P (X=x)
0.20
0.25
0.20
0.15
0.10
0.10

What is the standard deviation of X?
A.2.0
B.1.24
C.1.58
D.3.24

Question 7 of 20
0.0/ 1.0 Points
Find the variance of the following probability distribution.

X P(X)
1 0.30
2 0.15
3 0.05
4 0.25
5 0.25
A.1.73
B.1.61
C.2.60
D.1.27

Question 8 of 20
1.0/ 1.0 Points
The failure rate for taking the bar exam in Philadelphia is
41%. If 375 people take the bar exam, what is the mean for the number of
failures?
A.138.1
B.171.2
C.90.7
D.153.8

Question 9 of 20
1.0/ 1.0 Points
The binomial distribution can occur in which of the
following situations?

I. whenever
we are interested in the number of events that occur over a given interval of
time
II. whenever
we sample from a population with only two types of members
III. whenever
we perform a sequence of identical experiments, each of which has only two
possible outcomes
A.I only
B.I and II
C.II and III
D.All of the above

Question 10 of 20
1.0/ 1.0 Points
A discrete probability distribution:
A.can be estimated
from long-run proportions
B.is a tool that can
be used to incorporate uncertainty into models
C.lists all of the
possible values of the random variable and their corresponding probabilities
D.is the distribution
of multiple random variables

Part 3 of 6 – 3.0/
4.0 Points

Question 11 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

In a history class, students take a weekly multiple choice
quiz consisting of 6 questions, each with 4 possible answers. If a student
randomly guesses at the answer to each question for every quiz, then what is
the mean number of correct answers the student will get on each quiz?

example, 4.5 would be a legitimate entry.

Question 12 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

In a survey, 55% of the voters support a particular referendum.
If 40 voters are chosen at random, and X is the number of voters that support
this referendum, find the mean and variance of X. Place the mean in the first
blank Correct22 and place the variance
in the second blank. Correct9.9

Question 13 of 20
0.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

In February 2002 the Argentine peso lost 70% of its value
compared to the United States dollar. This devaluation drastically raised the
price of imported products. According to a survey conducted by AC Nielsen in
April 2002, 68% of the consumers in Argentina were buying fewer products than
before the devaluation, 24% were buying the same number of products, and 8%
less-expensive brands, 88% indicated that they had changed the brands they purchased.
Suppose the following complete set of results were reported. Use the following

Number of Products Purchased

Brands Purchased
Fewer
Same
More
Total
Same
10
14
24
48
Changed
262
82
8
352
Total
272
96
32
400

What is the probability that a consumer selected at random
rounded to 4 decimal places, in the blank.
Correct.6800

Question 14 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

Find the mean of the following probability distribution.

X 1 2 3 4 5
P(X) 0.20 0.10 0.35 0.05 0.30
example, 4.56 would be a legitimate entry.

Mean =
Correct3.15
Part 4 of 6 – 4.0/
4.0 Points

Question 15 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

Mothers Against Drunk Driving (MADD) is a very visible group
whose main focus is to educate the public about the harm caused by drunk
drivers. A study was recently done that emphasized the problem we all face with
drinking and driving. Five hundred accidents that occurred on a Saturday night
were analyzed. Two items noted were the number of vehicles involved and whether
alcohol played a role in the accident. The numbers are shown below:

Number of Vehicles Involved
Did alcohol play a role?
1
2
3
Yes
60
110
30
200
No
40
215
45
300

100
325
75

What proportion of accidents involved alcohol and a single
vehicle?
blank. For example, 0.23 is a legitimate entry.
Correct0.12

Question 16 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

An urn contains 12 balls identical in every respect except
their color. There are 3 red balls, 7 green balls, and 2 blue balls. You draw
two balls from the urn, but replace the first ball before drawing the second.
Find the probability that the first ball drawn is red and the second ball drawn
is green. Place your answer, rounded to 4 decimal places, in the blank. For
example, 0.4567 would be a legitimate entry.
Correct0.1458

Question 17 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

At a certain college, there were 600 science majors, 200
engineering majors, and 500 business majors. If a student is selected at
random, what is the probability that the student is an engineering major?

Place your
answer, rounded to four decimal places, in the blank. Correct0.1538 When entering your answer do not use any
labels or symbols other than a decimal point.
Simply provide the numerical value. For example, 0.1234 would be a
legitimate entry.

Question 18 of 20
1.0/ 1.0 Points
Accepted characters: numbers, decimal point markers (period
or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000),
“E” or “e” (used in scientific notation). NOTE: For
scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where
“a” and “b” need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is
valid whereas {9i} is not.

A lock on a bank vault consists of three dials, each with 30
positions, In order for the vault to open, each of the three dials must be in
the correct position. How many different “dial combinations” are
there for this lock? Place your answer in the blank. Do not use any decimal
places or commas. For example, 12345 would be a legitimate entry. Correct27000

Part 5 of 6 – 1.0/
1.0 Points

Question 19 of 20
1.0/ 1.0 Points
Suppose A and B are mutually exclusive events where P(A) =
0.3 and P(B) = 0.4, then P(A and B) = 0.12.

True
False

Part 6 of 6 – 1.0/
1.0 Points

Question 20 of 20
1.0/ 1.0 Points
The variance of a binomial distribution for which n = 50 and
p = 0.20 is 8.0.
Correct
True
False