Q1. Identify the statement as true or false.

10 - 5 = 5 if and only if 7 + 5 = 13.

a. True

b. False

Q2. Identify the statement as true or false.

2 + 1 = 6 if and only if 12 = 9.

a. False

b. True

Q3. Identify the statement as true or false.

10 + 1 = 13 if and only if 9 = 10.

a. False

b. True

Q4. Identify the statement as true or false.

6 + 1 = 3 if and only if 7 = 15.

a. False

b. True

Q5. Identify the statement as true or false.

5 x 2 = 14 if and only if 5 + 7 = 12.

a. False

b. True

Q6. Identify the statement as true or false.

8 x 2 = 20 if and only if 6 + 7 = 13.

a. True

b. False

Q7. what is a negation for the statement.

My brother is asleep.

a. The person who is asleep is not my brother.

b. My sister is awake.

c. My brother is not asleep.

d. My sister is asleep.

Q8. Identify the statement as true or false.

9 - 2 = 7 if and only if 11 + 3 = 15.

a. True

b. False

Q9. Decide whether the statement is compound.

The longest book I ever read was "War and Peace."

a. Not compound

b. Compound

Q10. what is a negation for the statement.

That athlete wants to be a musician.

a. That musician wants to be an athlete.

b. That athlete is not a musician.

c. That athlete does not want to be a musician.

d. That musician does not want to be an athlete.

Q11. For the given direct statement, write the indicated related statement (converse, inverse, or contrapositive).

If you like me, then I like you. (converse)

a. If you don't like me, then I don't like you.

b. If I don't like you, then you don't like me.

c. If I like you, then you like me.

d. I like you if you don't like me.

Q12. Identify the statement as true or false.

12 + 1 = 11 if and only if 5 = 9.

a. True

b. False

Q13. Identify the statement as true or false.

7 - 5 = 2 if and only if 11 + 4 = 16.

a. False

b. True

Q14. Find the number of subsets of the set.

{0, 9, 10, 11}

a. 16

b. 15

c. 8

d. 4

Q15. Identify the probability statement as empirical or not.

The probability that it will snow on December 25 in New York City is 0.20.

a. Not empirical

b. Empirical

Q16. Two dice are rolled. Write the indicated event in set notation.

The sum of the dice is a multiple of 3.

a. {(1, 2), (1, 5), (3, 3), (3, 6), (4, 5), (6, 6)}

b. {(1, 2), (2, 1), (2, 4), (4, 2), (1, 5), (5, 1), (3, 3), (3, 6), (6, 3), (4, 5), (5, 4), (6, 6)}

c. {(1, 3), (3, 1), (3, 3), (2, 3), (3, 2), (3, 4), (4, 3), (5, 3), (3, 5), (6, 3), (3, 6)}

d. {(3, 3), (6, 6)}

Q17. Use the rule of total probability to find the indicated probability.

Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 5% of its contents defective, while shipment II has 4% of its contents defective. If it is equally likely an employee will go to either bin and select a component randomly, what is the probability a selected component is defective?

a. 9

b. 0.09

c. 4.5

d. 0.045

Q18. Find the indicated probability.

The distribution of B.A. degrees conferred by a local college is listed below, by major.

MajorFrequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is in Engineering?

a. 0.0012

b. 0.0932

c. 0.1028

d. 868

Q19. Write the sample space for the given experiment.

A box contains 13 white cards numbered 1 through 13. One card with a number greater than 6 is chosen. and its number is recorded.

a. {11}

b. {6, 7, 8, 9, 10, 11, 12, 13}

c. {1, 2, 3, . . . , 13}

d. {7, 8, 9, 10, 11, 12, 13}

Q20. Use Bayes' rule to find the indicated probability.

Two stores sell a certain product. Store A has 30% of the sales, 2% of which are of defective items, and store B has 70% of the sales, 5% of which are of defective items. The difference in defective rates is due to different levels of pre-sale checking of the product. A person receives a defective item of this product as a gift. What is the probability it came from store B?

a. 0.8537

b. 0.1714

c. 0.1463

d. 1

Q21. Use Bayes' rule to find the indicated probability.

A person must select one of three boxes, each filled with clocks. The probability of box A being selected is 0.36, of box B being selected is 0.29, and of box C being selected is 0.35. The probability of finding a red clock in box A is 0.2, in box B is 0.4, and in box C is 0.9. A box is selected. Given that the box contains a red clock, what is the probability that box A was chosen?

a. 0.36

b. 0.133

c. 0.143

d. 0.072

Q22. Find the odds.

Find the odds in favor of rolling an odd number when a fair die is rolled.

a. 1 to 2

b. 2 to 1

c. 3 to 2

d. 1 to 1

Q24. Find the probability.

A calculator requires a keystroke assembly and a logic circuit. Assume that 80% of the keystroke assemblies and 82% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory. Assume that defects in keystroke assemblies are independent of defects in logic circuits.

a. .6724

b. .6560

c. .6400

d. .8100

Q25. Use Bayes' rule to find the indicated probability.

67% of the workers at Motor Works are female, while 63% of the workers at City Bank are female. If one of these companies is selected at random (assume a 50-50 chance for each), and then a worker is selected at random, what is the probability that the worker is female, given that the worker comes from City Bank?

a. 31.5%

b. 42.2%

c. 33.5%

d. 67%

Q26. Provide an appropriate response.

A sample space S is a set of 7 outcomes. What is the most distinct events that S can have?

a. 5040

b. 128

c. 7

d. 1

Q27. Evaluate the permutation.

P(10, 6)

a. 10

b. 1

c. 720

d. 151,200

Q28. Suppose there are 3 roads connecting town A to town B and 7 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

a. 21 ways

b. 49 ways

c. 9 ways

d. 10 ways

Q29. If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.

a. 10,000 licenses

b. 3024 licenses

c. 4960 licenses

d. 5040 licenses

Q30. Provide an appropriate response.

Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

a. Combination

b. Permutation

c. Neither

Q31. Find the requested probability.

What is the probability that 19 rolls of a fair die will show 6 fives?

a. .0272

b. .1088

c. .0544

d. .0109

Q32. A restaurant offered salads with 3 types of dressings and one choice of 5 different toppings. How many different types of salads could be offered?

a. 15 types

b. 9 types

c. 25 types

d. 8 types

Q33. Find the probability of the event.

A die is rolled 18 times and two threes come up.

a. .060

b. .230

c. .099

d. .160

Q34. How many distinguishable permutations of letters are possible in the word?

LOOK

a. 24

b. 12

c. 16

d. 4

Q35. To win the World Series, a baseball team must win 4 games out of a maximum of 7 games. To solve the problem, list the possible arrangements of losses and wins.

How many ways are there of winning the World Series in exactly 6 games if the winning team loses the first game?

a. 7 ways

b. 6 ways

c. 4 ways

d. 5 ways

Q36. In how many ways can a group of 6 students be selected from 7 students?

a. 6 ways

b. 42 ways

c. 7 ways

d. 1 way

Q37. In how many ways can a student select 8 out of 10 questions to work on an exam?

a. 45 ways

b. 16 ways

c. 100,000,000 ways

d. 90 ways

Q38. If 3 balls are drawn from a bag containing 3 red and 4 blue balls, what is the expected number of red balls in the sample?

a. 1.29

b. .89

c. 1.39

d. 1.54

Q39. A test can have grades from 0 to 100, inclusive. If 53 students take the test, is the median necessarily 50?

a. No

b. Yes

Q40. Find the mean. Round to the nearest tenth.

Value Frequency

163 2

216 2

265 7

313 6

333 3

389 1

a. 265.3

b. 80.0

c. 280.0

d. 309.4

Q41. A six-sided fair die is rolled n times. If you are concerned about the probability a 3 comes up a given number of times, can you consider this a Bernoulli trial in determining the desired probability?

a. Yes

b. No

Q42. Find a z-score satisfying the given condition.

20.1% of the total area is to the right of z.

a. .84

b. .82

c. .83

d. -.84

Q43. Solve the problem using the normal curve approximation to the binomial distribution.

A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

a. .4641

b. .5871

c. .4168

d. .0832

Q44. Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of the indicated results.

Less than 259 heads

a. .788

b. .224

c. .773

d. .776

Q45. Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent.

At a local market, the average weekly grocery bill is $57.85 with a standard deviation of $14.25. What is the lowest amount spent by the upper 25% of market customers?

a. $67.54

b. $67.82

c. $67.40

d. $9.55

Q46. Find the median.

5, 8, 17, 22, 30, 41, 49

a. 30

b. 25

c. 22

d. 17

Q47. If the life of a car engine, calculated in miles, is normally distributed, with a mean of 200,000 miles and a standard deviation of 18,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty?

a. Less than 238,110 miles

b. Less than 161,890 miles

c. Less than 184,460 miles

d. Less than 146,720 miles

Q48. Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent.

A certain grade egg must weigh at least 2.5 oz. If the average weight of an egg is 1.5 oz, with a standard deviation of .4 oz, how many eggs in a sample of 9 dozen would you expect to be over

the 2.5 oz size?

a. 5 eggs

b. 1 egg

c. 12 eggs

d. 2 eggs

Q49. Find the percent of the total area under the standard normal curve between the given z-scores.

z = -1.10 and z = -0.36

a. 0.2239

b. 0.4951

c. 0.2237

d. -0.2237

Q50. Solve the problem using the normal curve approximation to the binomial distribution.

Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

a. .0034

b. .0057

c. .0051

d. .0065