algebra 1b study guide (part b - probability and statistics) a. c

Algebra 1B Study Guide (Part B - Probability and Statistics)

Name: _______________________________________________ Date: __________

____ 1. After the introduction of a new soft drink, a taste test is conducted to see how it is beingreceived. Of those who participated, 64 said they preferred the new soft drink, 80 preferred theold soft drink, and 56 could not tell any difference. What is the probability that a person in thissurvey, chosen at random, preferred the new soft drink?

A. 45

C. 817

B. 49

D. 825

2. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Kelly tosses a penny, a nickel, and a dime all at once and records whether each lands heads up ortails up. Then he tosses a quarter and a half dollar together and records the result. How manydifferent overall results are possible?

3. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. In a survey of 230 students at Sequoia High School, 180 said their favorite type of television show isa reality-based show. Assume that the results of the survey are representative of all high schoolstudents. If Mike asks two randomly selected high school students to name their favorite type oftelevision show, what is a reasonable prediction of the probability that neither student will favorreality-based shows? Express your answer as a decimal rounded to the nearest hundredth.

Algebra 1B Study Guide (Part B - Probability and Statistics), Version: 1 1


4. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Suppose you spin each of the spinners below at the same time. How many possible outcomes arethere?



5. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. What is the total number of possible outcomes when one coin is tossed and one ten-sided die isrolled?

____ 6. A coin is tossed and a die is rolled. What is the probability that the coin shows tails and the dieshows a four?

A. 18

C. 112

B. 118

D. 14

____ 7. The sections on a spinner are numbered from 1 through 8. If the probability of landing on agiven section is the same for all the sections, what is the probability of spinning a number lessthan 4 or greater than 7 in a single spin?

A. 58

C. 38

B. 18

D. 12

____ 8. After a very large clinical trial of adults, researchers concluded that a new pain medicationdoes not relieve pain in 6% of adults. Suppose two adults are selected at random. Find theprobability that the new medication will not relieve pain for either of these people.

A. 0.0036 C. 0.12 B. 0.8836 D. 0.06

____ 9. A picnic cooler contains 5 sandwiches made with rye bread, 4 sandwiches made with wholewheat bread, 6 made with oat bread, and 3 made with onion rolls. If only the sandwiches onrye bread and onion rolls have mustard on them, what is the probability that a sandwichselected randomly from the cooler has mustard on it?

A. 49

C. 12

B. 45

D. 25



Each section of the spinner shown below has the same area. The spinner was spun 32 times.The results are shown in the table.

____ 10. For which color is the experimental probability of stopping on the color the same as thetheoretical probability?

A. Red C. Blue B. Green D. Yellow

____ 11. Eight people are entered in a race. If there are no ties, in how many ways can the first twoplaces come out?

A. 16 C. 112 B. 56 D. 28

Find the value:

____ 12. 4! A. 12 C. 120 B. 48 D. 24

____ 13. 6P1

A. 1.5 C. 6 B. 3 D. 12

____ 14. 6P5

A. 1440 C. 720 B. 360 D. 180

____ 15. Suppose a set of traffic lights located at three consecutive intersections along a road are setso that each has an equal probability of turning red, green, or yellow when you arrive at theintersection where the light is located. What is the probability that a driver will encounter 2green lights and 1 yellow light, in any order, when approaching these traffic lights?

A. 227

C. 29

B. 127

D. 19



____ 16. Suppose you are choosing a 6-digit personal access code. This code is made up of 4 digitschosen from 1 to 9, followed by 2 letters chosen from A to Z. Any of these digits or letters canbe repeated. Use the counting principle to find the total number of personal access codesthat can be formed.

A. 341,172 C. 4,435,236 B. 492,804 D. 39,917,124

____ 17. There are 64 teams in a soccer tournament. Each team plays until it loses one game. Thereare no ties. How many games are played? You may want to draw a diagram to look for apattern.

A. 62 games C. 64 games B. 65 games D. 63 games

18. Suppose you have just two pennies, two nickels, three dimes and three quarters in your pocket.Assuming that each coin is equally likely to be selected, in how many ways can you choose each ofthe following?a. one coinb. two coinsc. eight coinsd. nine coins

Find the value:

____ 19. 6C5

A. 36 C. 6 B. 30 D. 0

____ 20. 9C3

A. 756 C. 252 B. 84 D. 75

____ 21. 13C6

A. 1716 C. 10,296 B. 22,308 D. 1703



____ 22. In a class of 25 students, 18 have brown eyes. If two students are chosen at random, whichexpression will calculate the probability that both have brown eyes?

A. C.

B. D.

____ 23. A spinner is divided into 8 equal parts and numbered from 1 through 8. What is the probabilityof spinning a number less than 4 or greater than 7 in a single spin?

A. 38

C. 12

B. 18

D. 58

____ 24. A bag has 2 orange blocks and 5 yellow blocks. Cliff takes a block out of the bag at random,records the color, then replaces the block in the bag. He does this 70 times. Which answershows the results he is most likely to have?

A. 35 orange and 35 yellow C. 50 orange and 20 yellow B. 69 orange and 1 yellow D. 20 orange and 50 yellow



____ 25. A drawer contains 3 red socks, 5 white socks, and 7 blue socks. Without looking, you drawout a sock and then draw out a second sock without returning the first sock. What is theprobability that the first sock and the second sock are both blue?

A. 221

C. 49225

B. 19

D. 15

____ 26. A large company rates its employees every six months as either satisfactory orunsatisfactory. Employees who had any kind of previous work experience are more likely tobe rated as satisfactory than employees without previous work experience. The percents ofexperienced and inexperienced workers and their breakdown into satisfactory andunsatisfactory ratings are shown in the diagram below.

What is the probability that a randomly selected employee will be one who had noprevious work experience and is rated unsatisfactory? Round your answer to thenearest whole percent.

A. 13% C. 15% B. 8% D. 18%

____ 27. A drawer contains 3 red socks, 5 white socks, and 7 blue socks. Without looking, you drawout a sock and then draw out a second sock without returning the first sock. What is theprobability that both socks are blue?

A. 49225

C. 19

B. 221

D. 15

____ 28. A ceramic jar contains 18 nickels and 15 dimes. If two coins are randomly drawn insuccession, without replacement, what is the probability that the total value of the coins is$0.10?

A. 35176

C. 51176

B. 2788

D. 45176



____ 29. A bag contains 3 green marbles and 6 blue marbles. What is the probability of drawing a bluemarble, then another blue marble, then a green marble, replacing the marble after eachdraw?

A. 227

C. 53

B. 427

D. 43

____ 30. The weather report predicts a 40% chance of snow on Tuesday and a 50% chance onWednesday. Assuming these are independent events, what is the probability it will snow onlyon Wednesday?

A. 30% C. 20% B. 90% D. 50%

31. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. If the spinner below is spun twice, what is the probability that the arrow will stop on a vowel bothtimes?

____ 32. Which sampling method is most likely to give a representative sample of the opinions ofvoters in an election race for governor of a state?

A. Call 1000 randomly selected registeredvoters and ask their opinions.

C. Ask viewers of the 11:00 P.M. news on alocal television station to register theiropinions on the station's web site.

B. Over the course of a week, poll everycustomer who comes into a car dealershipand is willing to answer questions.

D. Send questionnaires to 500 randomlyselected registered members of each ofthe recognized political parties in the state.



____ 33. Which survey question is unbiased? A. "Does the school board have the right to

exclude unruly parents from PTAmeetings?"

C. "Do you think we should allow them to teardown lovely old homes to make room forthe new freeway?"

B. "Would you like fruit or french fries forlunch?"

D. "Do you think Smith is a good managereven though he has questionableopinions?"



____ 34. The graphs below show the number of honor-roll students in each grade at Ferndale MiddleSchool. Which statement is true?

A. The two graphs each give the reader thesame impression of the data.

C. Because the scale on the first graph doesnot begin at zero, it distorts the length ofthe bars.

B. The scale of the second graph ismisleading.

D. The first graph shows greater differencesin the number of honor-roll students thanthe second graph.



35. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. After looking quickly at the graph below in preparation for a sales meeting, the President ofNewmark Realty had the impression that the company had gained twice as many new clients inMarch as in January.

In decimal form, what is the ratio of the number of new clients gained in March compared tothe number gained in January?

____ 36. Name the mode or modes of the data.3, 12, 27, 5, 24, 10, 26, 29, 15, 22, 15

A. 15 C. 17.1 B. 24 D. 3, 29

____ 37. What are the mean, median, and mode(s) of the data?8, 22, 15, 2, 29, 27, 27, 16, 27, 26, 21

A. 20, 21.5, 27 C. 20, 22, 27 B. 22, 27, 20 D. 22, 20, 27

____ 38. So far in math class, a student's quiz scores are 86%, 82%, 72%, and 69%. What score doesthe student need on the fifth quiz to have a mean quiz score of 79%? All the quizzes haveequal weights.

A. 86% C. 79% B. 77.25% D. 87%



____ 39. The scores for the 33 participants in a fund-raising golf tournament are represented in thegraph below. In which interval is the median score found?

A. 70-79 C. 80-89 B. 90-99 D. 100-109

____ 40. Jake's test scores for the first term of chemistry class were 78, 68, 73, 94, and 62. Which ofthe measures of central tendency would make Jake's test scores seem as high as possible?

A. mode C. mean B. range D. median

____ 41. A building contractor must estimate her income for the next three months in order to file anestimated quarterly income tax form. In the last six months, her company has built and sold32 houses at prices of $145,000 or less and 6 houses at prices of $325,000 or more. Thecontractor expects the proportion of houses at each price range to continue to be vary similarover the next three months. Which measure of central tendency should she use to predictthe income from the 20 houses she expects to be able to build and sell in the next threemonths?

A. mean C. median B. mode D. range



42. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. For each of the three sets of numbers below, x represents the same measure of central tendency,either the mean, the median, or the mode of the data.Set 1: 28, 17, 20, 26, 23;x = 23 Set 2: 42, 19, 34, 25, 27, 31;x = 29 Set 3: 18, 23, 23, 19, 28;x = 23 Consider the set of numbers 28, 42, 42, 31, 35, and 33. If x represents the same measure of centraltendency as it does in the first three sets of numbers, what is the value of x for this set of numbers?

____ 43. You weigh six packages and find the weights to be 20, 12, 52, 16, 48, and 44 ounces. If youinclude a package that weighs 60 ounces, which will increase more, the median or the mean?

A. The median increases more. C. The mean increases more. B. The median and the mean will stay the

same. D. The median and mean are affected the

same amount.

____ 44. The weights of five trout caught in Lake Placid are 2 pounds 15 ounces, 1 pound 6 ounces, 1pound 1 ounce, 2 pounds 8 ounces, and 1 pound 6 ounces. What is the median weight of thefive fish?

A. 1 pound 15 ounces C. 1 pound 6 ounces B. 2 pounds 15 ounces D. 2 pounds 8 ounces

____ 45. Which list gives the median of each of the four sets of numbers below?Set 1: 5, 15, 25, 40, 40Set 2: 4, 20, 32, 36, 36, 58Set 3: 23, 28, 28, 28, 28Set 4: 15, 17, 17, 23, 25, 29

A. 40, 36, 28, 17 C. 25, 34, 28, 20 B. 25, 32, 28, 23 D. 25, 31, 27, 21



46. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Mr. Benson recorded the number of sick days taken last year by each employee, as shown in thetable.Employees Sick DaysKeisha 9Lynette 6Tyler 2Grace 7Kurt 3Dimitri 5Leah 2Lynn 5Ryan 5

What is the mean number of sick days taken by employees last year? Round your answer to thenearest hundredth.

____ 47. Which of the following is a list of the data represented by the stem-and-leaf plot below?2 6 8 83 4 7 74 0 1 5 55 2 3 9

A. 26, 34, 41, 52, 37, 53, 28, 45, 59, 40, 37,28, 45

C. 6, 8, 8, 4, 7, 7, 0, 1, 5, 5, 2, 3, 9

B. 28, 28, 24, 27, 37, 30, 31, 45, 45,42, 4, 53,59

D. 28, 2, 24, 27, 37, 30, 31, 45, 4,42, 4, 5, 59



48. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The students at Heritage High School collected toys for a children's center. The stem-and-leaf plotshows the class totals of the number of toys collected. Rounded to the nearest whole percent, whatpercent of the classes collected more than 46 toys?

____ 49. Ann records how many push-ups she and several of her friends can do in one minute. Whichstem-and-leaf plot represents the data she collected?15, 18, 19, 11, 10, 30, 16, 16, 15, 19

A. Stem Leaf1 0 1 5 5 6 6 8 923 0 9

C. Stem Leaf1 0 1 5 5 6 6 8 9 923 0

B. Stem Leaf1 0 1 5 6 6 8 9 923 0

D. Stem Leaf1 0 1 5 5 6 8 9 923 0

____ 50. Only one of the box-and-whisker plots correctly displays data about the ages of teammembers on a company baseball team. The statements below are all true about the team.Use the statements to correctly choose the box-and-whisker plot.• The youngest member is 20 years old.• About 75% of the members are between 25 and 34 years old.• No one is older than 34 years old.• About 50% of the members are at least 29 years old.

A. C.

B. D.



51. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Yvette made the following stem − and − leaf plots of the high and low temperatures for 10 days.

LowsStem Leaf3 33204 8545 9436

HighsStem Leaf3 7745 12556 1336

How much greater was the highest temperature than the lowest temperature?

____ 52. Find the range of the data in the stem-and-leaf plot.

A. 54 C. 34 B. 33 D. 55

____ 53. Draw a box-and-whisker plot of the data. 31, 26, 12, 25, 34, 30, 18 A. C.

B. D.



____ 54. Which data are represented by the box-and-whisker plot?

A. 28, 23, 9, 22, 33, 27, 15 C. 28, 21, 9, 22, 31, 27, 15 B. 28, 23, 9, 14, 31, 27, 15 D. 28, 23, 9, 22, 31, 27, 15

____ 55. Fifteen mothers were asked how many months old their babies were when they cut their firsttooth. The results are shown below.6, 8, 7, 7, 10, 10, 7, 5, 7, 9, 7, 6, 10, 1, 7Find the range and the outlier(s), if any, of the data set.

A. range 10; no outliers C. range 9; no outliers B. range 9; outlier 1 D. range 10; outlier 1

____ 56. Thirteen golfers were asked what their score was on their last game. The scores are shownbelow.73, 83, 83, 73, 72, 72, 82, 86, 74, 87, 80, 89, 81Find the range and the outlier(s), if any, of the golfers' scores.

A. range 16; no outliers C. range 16; outlier 89 B. range 17; no outliers D. range 17; outlier 72

____ 57. Thirteen bowlers were asked what their score was on their last game. The scores are shownbelow.171, 181, 174, 203, 175, 177, 177, 181, 171, 180, 170, 170, 177Find the range and outlier(s), if any, of the bowlers' scores.

A. range 32; no outliers C. range 33; outlier 203 B. range 32; outlier 203 D. range 33; no outliers



Answer Key

1. D. 825

Keywords probability word

2. 32

Keywords counting principle word real-life

Standards NCTM 9-12.NOP.2.c NCTM 9-12.DAP.4.e

3. 0.05Note that variations in rounding could result in slightly different answers.

Keywords group probability sample predict

4. 168

Keywords count counting principle outcomes

Standards NCTM 9-12.DAP.4.e

5. 20

Keywords probability


6. C. 112



Keywords event compound probability


7. D. 12

Keywords probability event mutually exclusive

8. A. 0.0036

Keywords probability independent

9. A. 49

Keywords probability word real-life compound

10. B. Green

Keywords theoretical probability experimental probability application

Standards TX TAKS 9 TX TEKS 8.11.B

11. B. 56


12. D. 24

Keywords factorial


13. C. 6

Keywords permutation




14. C. 720

Keywords permutation


15. D. 19

Keywords probability list word real-life tree diagram

16. C. 4,435,236

Keywords count counting principle outcomes

Standards NCTM 9-12.NOP.2.c

17. D. 63 games

Keywords data probability table

Standards NCTM 9-12.NOP.2.c

18. a. 10; b. 45; c. 45; d. 10

Keywords word combination Pascal's triangle


19. C. 6

Keywords combination factorial


20. B. 84

Keywords



combination factorial


21. A. 1716

Keywords combination factorial


22. D.

Keywords formula combination probability


23. C. 12

Keywords event mutually exclusive probability disjoint


24. D. 20 orange and 50 yellow

Keywords probability proportion outcome experiment

Standards NCTM 9-12.DAP.4.d NCTM 9-12.DAP.4.e

25. D. 15

Keywords



probability dependent event

26. B. 8%

Keywords word real-life tree diagram probability


27. D. 15

Keywords probability dependent event

28. C. 51176

Keywords dependent probability


29. B. 427

Keywords probability multiplication independent event rule discrete


30. A. 30%

Keywords probability independent word mutually exclusive

Standards NCTM 9-12.DAP.4.d NCTM 9-12.DAP.4.e

31. 1 / 4

Keywords



probability spinner compound

Standards NCTM 9-12.DAP.4.e NCTM 9-12.REP.1

32. A. Call 1000 randomly selected registered voters and ask their opinions.

Keywords sample random word real-life method survey poll

Standards NCTM 9-12.DAP.1.b

33. B. "Would you like fruit or french fries for lunch?"

Keywords survey question bias

Standards NCTM 9-12.DAP.1.b

34. C. Because the scale on the first graph does not begin at zero, it distorts the length of thebars.

Keywords data graph misleading

35. 1.5 ">

Keywords graph misleading bar graph

Standards NCTM 9-12.REP.1

36. A. 15

Keywords mode

Standards NCTM 9-12.DAP.1.e NCTM 9-12.DAP.2.a

37. C. 20, 22, 27

Keywords mode



mean median


38. A. 86%

Keywords mean set guess check


39. C. 80-89

Keywords mode solve word mean median range central tendency


40. C. mean

Keywords word real-life mean median central tendency data mode


41. A. mean

Keywords mode appropriate word real-life mean median range determine central tendency

Standards



NCTM 9-12.DAP.2.a

42. 34

Keywords mean median central tendency

Standards NCTM 9-12.DAP.1.e NCTM 9-12.DAP.2.d NCTM 9-12.DAP.2.a NCTM 9-12.REP.1

43. A. The median increases more.

Keywords word mean median analyze central tendency sample

Standards NCTM 9-12.DAP.2.a

44. C. 1 pound 6 ounces

Keywords statistics word median


45. C. 25, 34, 28, 20

Keywords identify median data


46. 4.89

Keywords data average table mean

Standards NCTM 9-12.DAP.1.e NCTM 9-12.DAP.2.a NCTM 9-12.REP.1

47. A. 26, 34, 41, 52, 37, 53, 28, 45, 59, 40, 37, 28, 45

Keywords plot



stem-and-leaf

48. 53

Keywords word real-life interpret stem-and-leaf percent

Standards NCTM 9-12.REP.1

49.

C.

Stem Leaf1 0 1 5 5 6 6 8 9 923 0

Keywords data representation missing stem-and-leaf

50. C.

Keywords box-and-whisker data

Standards NCTM 9-12.DAP.1.d

51. 36 °

Keywords plot stem leaf interpret


52. C. 34

Keywords range stem-and-leaf




53. B.

Keywords box-and-whisker plot

Standards NCTM 9-12.DAP.1.d NCTM 9-12.DAP.2.a

54. D. 28, 23, 9, 22, 31, 27, 15

Keywords box-and-whisker plot

Standards NCTM 9-12.DAP.1.d

55. B. range 9; outlier 1

Keywords range outlier data


56. B. range 17; no outliers

Keywords data range outlier


57. C. range 33; outlier 203

Keywords range outlier data




Standards Summary

NCTM 9-12.NOP.2.c develop an understanding of permutations and combinations ascounting techniques.

NCTM 9-12.DAP.4.e understand how to compute the probability of a compound event.

TX TAKS 9 The student will demonstrate an understanding of percents,proportional relationships, probability, and statistics in applicationproblems.

TX TEKS 8.11.B use theoretical probabilities and experimental results to makepredictions and decisions; and

NCTM 9-12.DAP.4.d understand the concepts of conditional probability andindependent events;

NCTM 9-12.REP.1 Create and use representations to organize, record, andcommunicate mathematical ideas

NCTM 9-12.DAP.1.b know the characteristics of well-designed studies, including therole of randomization in surveys and experiments;

NCTM 9-12.DAP.1.e compute basic statistics and understand the distinction betweena statistic and a parameter.

NCTM 9-12.DAP.2.a for univariate measurement data, be able to display thedistribution, describe its shape, and select and calculatesummary statistics;

NCTM 9-12.DAP.2.d recognize how linear transformations of univariate data affectshape, center, and spread;

NCTM 9-12.DAP.1.d understand histograms, parallel box plots, and scatterplots anduse them to display data;


algebra 1b study guide (part b - probability and statistics) a. c

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