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Math 302 quiz 2 2019 (already graded)

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Part 1 of 6 –         5.0/ 5.0 Points

Question 1 of 20               1.0/ 1.0 Points

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.1/600

                  B.1/2300

                  C.1/300

                  D.1/700

Answer Key:

Question 2 of 20               1.0/ 1.0 Points

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

                  A.0.25

                  B.0.90

                  C.0.40

                  D.Cannot be determined from the information given  

Answer Key:

Question 3 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 Law of Large Numbers   

                  B.the Empirical Rule

                  C.the Central Limit Theorem

                  D.subjective probabilities

Answer Key:

Question 4 of 20               1.0/ 1.0 Points

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

Answer Key:

Question 5 of 20               1.0/ 1.0 Points

If P(A) = P(A|B), then events A and B are said to be

                  A.mutually exclusive

                  B.complementary

                  C.independent

                  D.exhaustive

Answer Key:

Part 2 of 6 –         5.0/ 5.0 Points

Question 6 of 20               1.0/ 1.0 Points

A multiple choice quiz consists of 6 questions, each with 4 possible answers. If a student guesses at the answer to each question, then the mean number of correct answers is

                  A.6.00

                  B.1.50

                  C.4.00

                  D.10.00

Answer Key:

Question 7 of 20               1.0/ 1.0 Points

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 25 batteries will last at least 8 hours?

                  A.0.0009

                  B.0.9991

                  C.0.8967

                  D.0.0024

Answer Key:

Question 8 of 20               1.0/ 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

Find P( X   3)

                  A.0.80

                  B.0.85

                  C.0.15

                  D.0.20

Answer Key:

Question 9 of 20               1.0/ 1.0 Points

A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled.

                  A.60

                  B.50

                  C.7.1

                  D.5.9

Answer Key:

Question 10 of 20             1.0/ 1.0 Points

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

                  A.0.081

                  B.0.243

                  C.0.027

                  D.0.003

Answer Key:

Part 3 of 6 –         2.0/ 4.0 Points

Question 11 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? Place your answer, rounded to 4 decimal places, in the blank.  .7443

Answer Key: 

Question 12 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.

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 =    2.26  

Answer Key:

Feedback: Mean = (1)(0.20) + (2)(0.10) + (3)(0.35) + (4)(0.05) + (5)(0.30) = 3.15

Comment: This is a distribution, to find the mean, you find

E = sumx * P(x)

I have shared with you videos on how to do this in the examples in the discussion last week,

Question 13 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 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.   0.6550

Answer Key: 

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.

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.   0.54

Answer Key: 

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.

A restaurant menu has a price-fixed complete dinner that consists of an appetizer, entrée, beverage, and dessert. You have a choice of five appetizers, ten entrees, three beverages, and six desserts. How many possible complete dinners are possible? Place your answer, as a whole number—no decimal places—in the blank. For example 176 would be a legitimate entry  900

Answer Key:

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 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 sold on a cone and was vanilla flavor.Place your answer, rounded to 2 decimal places, in the blank. For exampe, 0.34 would be a legitimate entry.  0.10

Answer Key:

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.

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.  0.30

Answer Key:

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.

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 strawberry 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.  0.3825

Answer Key:

Comment: You got the previous one

Part 5 of 6 –         0.0/ 1.0 Points

Question 19 of 20             0.0/ 1.0 Points

Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.5, then P(A or B) = 0.70.

                  True

  False

Answer Key:

Part 6 of 6 –         1.0/ 1.0 Points

Question 20 of 20             1.0/ 1.0 Points

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

 True

  False

Answer Key:

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