A+ Answers




Question 1

If the probability that it will rain tomorrow is 0.38, then the probability that it will not rain tomorrow is:

A.0.38

B.-0.38

C.0.62

D.1.38

Question 2

A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is

A.5

B.8

C.15

D.30

Question 3

If a die is rolled one time, find the probability of getting a number greater than 2.

A.2

B.-1

C.5/6

D.4/6


Question 4

The formal way to revise probabilities based on new information is to use:

A.unilateral probabilities

B.complementary probabilities

C.conditional probabilities

D.common sense probabilities


Question 5

What type of probability uses sample spaces to determine the numerical probability that an event will occur?

A.empirical probability

B.conditional probability

C.classical probability

D.subjective probability


Part 2 of 6 –

Question 6

A researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 30 students: 12 of them supported the change, 13 of them did not, and 5 had no opinion. This is not a binomial model because…

A….less than half of the students supported the change.

B….there are 3 possible outcomes, not 2.

C.30 students are not enough for a good sample

D….the students who strongly supported the change and those who only mildly supported the change are counted the same.


Question 7

The probability distribution associated with the number of cartoons watched by Mrs. Kelly’s first grade class on Saturday morning is shown below.

 x  P(x)

0 0.15

1 0.20

2 0.30

3 0.10

4 0.20

5 0.05

      Find the standard deviation for the probability distribution above.

A.1.46

B.2.25

C.1.89

D.1.18


Question 8

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 variance of X?

A.3.42

B.4.32

C.2.34

D.2.50


Question 9

Find the variance of the following probability distribution.

X P(X)

1 0.20

2 0.35

3 0.10

4 0.25

5 0.10

A.1.83

B.1.31

C.1.25

D.1.71


Question 10

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 expected value of X?

A.1.20

B.3.65

C.2.0

D.6.25


Part 3 of 6 –

Question 11

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.

If a gambler rolls two dice and gets a sum of four, he wins $10; and if he gets a sum of three, he wins $25. The cost to play the game is $5. What is the expectation of this game?

Place your answer, rounded to two decimal places, in the blank.  -2.78  When entering your answer do not use a dollar sign. However, if the expected payoff is negative be sure to use a minus sign. For example, -1.23 would be a legitimate entry.

Question 12

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? Place your answer, rounded to 4 decimal places, in the blank. 0.6800

Question 13

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 22 and place the variance in the second blank. 9.90

Question 14

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.

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 6

P (X=x) 0.55 0.15 0.10 0.10 0.04 0.03 0.03

What is the expected value of X? Place your answer, rounded to two decimal places in the blank. For example, 4.56 would be a legitimate entry. 1.14

Part 4 of 6 –

Question 15

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.

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. What is the probability that at least two of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry. 0.352

Question 16

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.

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. What is the probability that none of the three vice presidents can attend the meeting? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.123 would be a legitimate entry. 0.216

Question 17

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 ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was vanilla flavor, given that it was sold in a cup.  Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry. 0.392

Question 18

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.

According to an Internet posting, 80% of adults enjoy drinking beer. If a group of 3 adults is selected at random, find the probability that none of them enjoy drinking beer.     

Place your answer, rounded to three decimal places, in the blank.  0.008 When entering your answer do not use any labels or symbols other than a decimal point.   Simply provide the numerical value. For example, 0.123 would be a legitimate entry.

Part 5 of 6 –

Question 19

True or False: Two events are mutually exclusive if they cannot occur at the same time.

True

False

Question 20

True or False: The probability of a success must remain the same for each trial in a binomial experiment.

True

False