## AMU MATH 302 quiz week 2 statistics American Military University

## AMU MATH 302 quiz week 2 answers

## AMU MATH 302 quiz week 2 Question 1

The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The

events A and B are:

A. mutually exclusive

B. unilateral

C .independent

D. conditional Reset Selection

## AMU MATH 302 quiz week 2 Question 2

Which of the following statements are true?

A.Probabilities can either be positive or negative.

B.Probabilities must be negative.

C. Probabilities must be nonnegative.

D.Probabilities can be any positive value. Reset Selection

## AMU MATH 302 quiz week 2 Question 3

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:

A.0.40

B.0.90

C. Cannot be determined from the information given

D. 0.25

## AMU MATH 302 quiz week 2 Question 4

The probability of an event and the probability of its complement always sum to:

A.any value between 0 and 1

B.0

C.1.0

D.any positive value

## AMU MATH 302 quiz week 2 Question 5

If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys

exactly 2 tickets.

A.1/700

B.1/300

C.1/2300

D.1/600

## AMU MATH 302 quiz week 2 Question 6

In one town 33% of the households have a vehicle with all-wheel drive. If 4 households are selected at random, what is the

probability that all 4 have vehicles with all-wheel drive?

A.0.33

B.0.0825

C.0.0119

D.0.4662

## AMU MATH 302 quiz week 2 Question 7

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating

with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that fewer than 40 batteries will last at least 8 hours?

A.0.9598

B.0.9211

C.0.7986

D.0.0789

## AMU MATH 302 quiz week 2 Question 8

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each

question has four possible choices.

A.0.19

B.0.17

C.0.08

D.0.23

## AMU MATH 302 quiz week 2 Question 9

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating

with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that greater than 30 batteries will last at least 8 hours?

A.0.9522

B.0.8594

C.0.0848

D.0.9152 Reset Selection

## AMU MATH 302 quiz week 2 Question 10

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

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

D.30 students are not enough for a good sample Reset Selection

## AMU MATH 302 quiz week 2 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.

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.

## AMU MATH 302 quiz week 2 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.

Find the mean of the distribution shown below.

X 0 1 2

P(X) 0.24 0.31 0.45

Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.

## AMU MATH 302 quiz week 2 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.

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

Find P(1 < X < 5). Place your answer, rounded to two decimal places in the blank. For example, 0.56 would be a legitimate entry.

## AMU MATH 302 quiz week 2 Question 14

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.Ann is applying for a bank loan to open a pizza franchise. She must first complete a written application and then, if the written application is approved, be interviewed by bank officers. If an applicant’s written application is not approved the applicant is not granted an interview with the bank officers. Past records for this bank show that the probability of an applicant having his or her written application approved is 0.63. Records also indicate that the interviewing committee of bank officers approves 85% of the individuals they interview. Find the probability that Ann’s loan request is approved. Place your answer, rounded to 2 decimal places, in the blank. For example, 0.76 would be a legitimate entry.

## AMU MATH 302 quiz week 2 Question 15

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

Given alcohol was involved, what proportion of accidents involved a single vehicle?

Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.

## AMU MATH 302 quiz week 2 Question 16

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:

f$A_{1}f$ = chocolate chosen

f$A_{2}f$ = strawberry chosen

f$A_{3}f$ = vanilla chosen

f$Bf$ = ice cream on a cone

f$ar{B}=f$ ice cream in a cup

Find the probability that the ice cream 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.

## AMU MATH 302 quiz week 2 Question 17

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 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:

f$A_{1}f$ = chocolate chosen

f$A_{2}f$ = strawberry chosen

f$A_{3}f$ = vanilla chosen

f$Bf$ = ice cream on a cone

f$ar{B}=f$ ice cream in a cup

Find the probability that the ice cream was strawberry flavor, given that it was sold on a cone. Place your answer, rounded to 4

decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Solution:

Solution:

In table:

conecup

Choc 45% 75% 25%

SBerry 30% 60% 40%

vanilla 25% 40% 60%

Probability of the following choices

AMU MATH 302 quiz week 2 Question 18

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 bag contains 12 colored balls, each ball being either black or white. The probability of drawing a white ball twice withreplacement is 1/16. How many white balls are in the bag? Place your answer in the blank, do not include any decimals or other marks. For example, 7 would be a legitimate entry.

There are white balls in the bag.

## AMU MATH 302 quiz week 2 Question 19

True or False: When rolling two dice, the outcomes “doubles” and “totals 7” are mutually exclusive.

True

False

## AMU MATH 302 quiz week 2 Question 20

A binomial experiment has exactly two outcomes, so the probability of any binomial experiment is always 0.5 or 50%.

True

False