# apu math302 quiz 2 done on april 2015

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?

Round your answer to one decimal place as necessary. For

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%

were buying more products. Furthermore, in a trend toward purchasing

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

data to answer this question.

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

purchased fewer products than before and changed brands? Place your answer,

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

Round your answer to two decimal place as necessary. For

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?

Place your answer, rounded to 2 decimal places, in the

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

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