Q1. 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.

Q2. Identify the statement as true or false.

14 + 1 = 4 if and only if 4 = 6.

a. False

b. True

Q3. select 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.

Q4. Write the statement in the formif p, then q: I go to class only if you go to class.

a. If you go to class, then I go to class.

b. If I go to class, then you go to class.

c. If I go to class, then you don't go to class.

d. If I don't go to class, then you don't go to class.

Q5. Identify the statement as true or false.

8 - 4 = 4 if and only if 10 + 5 = 16.

a. True

b. False

Q6. Identify the statement as true or false.

11 - 2 = 9 if and only if 7 + 5 = 13.

a. False

b. True

Q7. Identify the statement as true or false.

6 x 2 = 16 if and only if 6 + 9 = 15.

a. True

b. False

Q8. Identify the statement as true or false.

8 x 2 = 20 if and only if 5 + 7 = 12.

a. True

b. False

Q9. Identify the statement as true or false.

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

a. False

b. True

Q10. Identify the statement as true or false.

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

a. True

b. False

Q11. Identify the statement as true or false.

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

a. True

b. False

Q12. Write the statement in the formif p, then q: Practice is necessary for making the team.

a. If you don't make the team, then you don't practice.

b. If you make the team, then you don't practice.

c. If you make the team, then you practice.

d. If you practice, then you make the team.

Q13. Identify the statement as true or false.

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

a. False

b. True

Q14. 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

Q15. 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

Q16. Determine whether the given events are mutually exclusive.

Having good reading skills and having good math skills

a. No

b. Yes

Q17. 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

Q18. 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

Q19. Provide an appropriate response.

A sample space S is a set of 8 outcomes. What is the most distinct events that S can have?

a. 40,320

b. 8

c. 256

d. 1

Q20. Determine whether the given events are mutually exclusive.

Getting an A in your statistics course and getting a B in your statistics course.

a. Yes

b. No

Q21. Use the rule of total probability to find the indicated probability.

A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 4% of its contents being winners, while 2% of the contents of box B are winners. Box A contains 20% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is chosen at random, what is the probability it is a winner?

a. 0.024

b. 0.008

c. 0.06

d. 0.03

Q22. 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)}

Q23. Find the number of subsets of the set.

{0, 9, 10, 11}

a. 16

b. 15

c. 8

d. 4

Q24. 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

Q25. 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

Engineering868

9313

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

a. 0.0012

b. 0.0932

c. 0.1028

d. 868

Q26. Use Bayes' rule to find the indicated probability.

Two stores sell a certain product. Store A has 26% of the sales, 1% of which are of defective items, and store B has 74% of the sales, 2% 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. 0.8706

b. 0.9867

c. 0.1733

d. 0.1529

Q27. 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

Q28. Find the requested probability.

A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes?

a. .4441

b. .0536

c. .5362

d. .0594

Q30. 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

Q31. 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

Q32. 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 7 games if the winning team wins the first two games?

a. 10 ways

b. 5 ways

c. 4 ways

d. 3 ways

Q33. 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

Q34. 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

Q35. Provide an appropriate response.

Consider determining how many possible phone numbers are in an area code (repeated numbers allowed). Is this a combination, a permutation, or neither?

a. Neither

b. Combination

c. Permutation

Q36. How many distinguishable permutations of letters are possible in the word?

LOOK

a. 24

b. 12

c. 16

d. 4

Q37. 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

Q38. Find the requested probability.

A coin is biased to show 40% heads and 60% tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses?

a. 36%

b. 40%

c. 60%

d. 20%

Q39. 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

Q40. Find a z-score satisfying the given condition.

25.1% of the total area is to the right of z.

a. -.68

b. -.67

c. .33

d. .67

Q41. 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

Q42. 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

Q43. 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

Q44. Find the standard deviation.

50, 48, 20, 70, 41, 31, 40, 81, 63

a. 18.2

b. 6.2

c. 20.6

d. 19.3

Q45. Find the mode or modes.

20, 34, 46, 34, 49, 34, 49

a. 49

b. 46

c. 38

d. 34

Q46. Find the percent of the total area under the standard normal curve between the given z-scores.

z = 0.07 and z = 2.45

a. 0.4650

b. 0.5208

c. 0.6531

d. -0.4650

Q47. Find the median.

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

a. 30

b. 25

c. 22

d. 17

Q48. 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

Q49. 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

Q50.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