Name: ____________________________ Period: ____________

Advanced Unit 6:

STATISTICS & PROBABILITY

Chapter Questions

1. How can the collection, organization and display of data help to

interpret, evaluate inferences and make predictions about real-life situations and circumstances?

2. How does probability relate to real world application problems?

3. How do permutations and combinations fit into word problems?

4. How are different events classified and what can I use to solve them?

5. How can finding the ways to count the possible outcomes of compound events be used to determine their probability?

This is a calculator

friendly unit!

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Sampling

Classwork

1) In a survey of 300 voters, 68 said they voted for Candidate A. How many votes can Candidate A expect to receive if the population of the town is 10,000?

2) In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears are in the population?

3) From a survey of 100 commuters about how they get to work, 38 said they drive their cars, 47 said they take the bus, 14 said they take the subway, and 1 said they ride their bicycle. Out of 4,800 commuters, predict how many will commute to work in each of the following way.

a. Car b. Bus c. Subway d. Bicycle

4) To determine the consistency of a printer, 100 printed sheets are randomly checked and 4 sheets are defective. Is this sample reliable? About how many defective sheets would be expected if 2,400 sheets were printed?

5) The cafeteria employees would like to start selling fruit in the morning. They surveyed 24 students by asking every 8th student that entered the cafeteria for breakfast. Four students said they preferred apples, 3 preferred oranges, and 1 preferred peaches. If 336 students purchase breakfast daily, about how many students can they expect to pick an orange?

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Homework

6) In a capture-recapture study, 83 mountain lions were tagged and released back into the wild. Several months later, 300 mountain lions were captured, of which 54 were tagged. About how many mountain lions are in the population?

7) In a survey of 1056 voters at Roberts School, 274 said they voted for Candidate A. How many votes can Candidate A expect to receive if there were 5,101 votes?

8) From a survey of 80 students about their favorite subjects, 24 said Language Arts, 16 said Science, 31 said Mathematics, and 9 said Social Studies. Out of 960 students, predict how many will favor each subject.

a. Language Arts b. Science c. Mathematics d. Social Studies

9) A DVD player manufacturing company wants to test the quality of their DVD players. They randomly pick 50 DVD players to test and determine that 4 are defective. Is this sample reliable? About how many defective DVD players would you expect if 1,000 DVD players are made?

10) A library wants to expand their children’s book section. The librarians surveyed 30 children by asking every 6th child that visited the library to figure out what genres were most popular. The children’s responses were: 12 liked fiction, 8 liked non-fiction, 4 liked science fiction, and 6 liked mystery. If the library expects 540 children to visit the library in a week, about how many children will check out a mystery book?

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Comparing Two Populations

Classwork Use the following data to answer the next set of questions. Round your answers to the nearest hundredths.

Number of Students per Class at the Local Community College x x x x x x x x x x x x x x 30 31 32 33 34 35 36 37 38 39 40

Number of Students per Class at the State College x x x x x x x x x x x x x x x x x x x x 30 31 32 33 34 35 36 37 38 39 40

11) What is the mean number of students per class at the local community college?

12) What is the mean number of students per class at the state college?

13) What is the difference of the means?

14) What is the mean absolute deviation of the data set for the local community college?

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15) What is the mean absolute deviation of the data set for the state college?

16) Which college has more variability in the number of students it has per class? Explain your answer.

17) The difference of the means is approximately _____ times the mean absolute deviation of the data for the local community college.

18) The difference of the means is approximately _____ times the mean absolute deviation of the data for the state college.

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Homework Use the following data to answer the next set of questions. Round your answers to the nearest hundredths.

Points Earned per Game for the Timberwolves x x x x x x x x x x x x x x x x 0 1 2 3 4 5 6 7 8 9 10

Points Earned per Game for the Little Giants x x x x x x x x x x x x x x x x 0 1 2 3 4 5 6 7 8 9 10

19) What is the mean number of points earned by the Timberwolves per game?

20) What is the mean number of points earned by the Little Giants per game?

21) What is the difference of the means?

22) What is the mean absolute deviation of the data set for the Timberwolves?

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23) What is the mean absolute deviation of the data set for the Little Giants?

24) Which team has more variability in the number of points it earns per game? Explain your answer.

25) The difference of the means is approximately _____ times the mean absolute deviation of the data for the Timberwolves.

26) The difference of the means is approximately _____ times the mean absolute deviation of the data for the Little Giants.

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Introduction to Probability

Classwork A jar contains 6 red, 8 blue, one white, 7 black, and two yellow marbles. Use this information to determine the probability of selecting:

27) a white marble

28) a red marble

29) a yellow marble

30) a purple marble

31) a black marble

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Homework A spinner is divided into 8 sections of equal size. The sections are numbered 1 through 8. Use this information to determine the probability of the needle landing on:

32) section 7

33) an even numbered section

34) section 1, 2, 3, or 4

35) section 9

36) section 8

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Experimental and Theoretical Probability

Classwork

37) A die is rolled. Complete the table.

Roll Theoretical Probability

1

2

3

4

5

6

38) A die is rolled 10 times and the outcomes are:

Outcome Number of Times

Roll 1 0 Roll 2 3 Roll 3 1 Roll 4 3 Roll 5 2 Roll 6 1

Use the above table to find the experimental probability for the following questions.

a. rolling a 1

b. rolling a 2

c. rolling a 3

d. rolling a 4

e. rolling a 5

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Homework

A spinner contains 8 equally divided sections, two sections have the letter A, 3 sections have the letter B, one section has the letter C, one section has the letter D, and one section has the letter E.

39) Draw a picture of the spinner in the space to the right.

40) Use your drawing to fill in the chart.

Spin Theoretical Probability

A

B

C

D

E

41) The spinner is spun 10 times and the outcomes are:

Outcome Number of Times

A 4 B 1 C 3 D 2 E 0

Use the table above to find the experimental probability for the following questions.

a. spinning an A

b. spinning a B

c. spinning a C

d. spinning a D

e. spinning an E

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Word Problems

Classwork

42) You made 8 out of 15 shots on goal. Use experimental probability to predict how many goals you will make tomorrow if you take 70 shots.

43) There are 1000 buttons in the jar. You randomly select 10 buttons and get 3 red, 4 blue, 2 white, 1 black. Use experimental probability to predict how many buttons in the jar are:

a. Red b. Blue c. White d. Black

44) A die is rolled. What is the theoretical probability for rolling a 3? Mary rolls a die six times and rolls a 3, on two of the rolls. What is the experimental probability for rolling a 3?

45) Create a situation where the experimental probability and the theoretical probability have the same value.

46) A coin is flipped. What is the theoretical probability for flipping a tail? Mark and John flip a coin twenty times and get 8 heads, 12 tails. What is the experimental probability for flipping a tail? If Mark & John flip the coin 100 times, what do you think will happen to the experimental probability?

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Homework

47) Bart makes 20% of his free throws. If he takes 500 free throws, how many go in the basket? Predict how many baskets Bart makes when he takes 25 free throws.

48) A factory produces 1000 light bulbs per minute. Each minute, one bulb produced will be defective. What is the theoretical probability of selecting the defective bulb from the light bulbs produced in one minute? What is the theoretical probability of selecting a defective bulb from the light bulbs produced in one hour?

49) Every 100th box of candy contains a prize. What is the theoretical probability for selecting the box of candy with a prize? A case contains 1000 boxes and how many prizes? What is the probability of selecting a box containing a prize from a case?

50) Create a situation where the experimental probability is greater than the theoretical probability.

51) How does understanding probability help someone who plays cards?

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Fundamental Counting Principle

Classwork

52) A restaurant has 4 appetizers, 9 entrees, and 5 dessert choices. How many meals are possible? If the restaurant wants to increase their meals as much as possible by adding one more item, should they add an appetizer, an entrée or a dessert?

53) Martha has 8 shirts, 6 pair of pants, and 4 different pair of shoes. Assuming everything matches, how many days can Martha go without wearing the same outfit?

54) How many different 7 digit telephone numbers are there, if the first digit cannot be 0?

55) By adding an area code to each 7 digit telephone number, the phone company now has how many telephone numbers to choose from? (Remember that the first digit in the area code and the phone number itself cannot be 0.)

56) One state is considering creating license plates where letters cannot be repeated. If the state currently has license plates consisting of three letters, followed by three different digits, how many fewer license plates will be available when repetition of letters is not allowed?

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Homework

57) A phone comes in 12 different colors, 5 different head sets, and 7 different styles. How many different phones are available?

58) Mark is taking a 10 question, True/False quiz. How many different ways can the quiz be answered?

59) Frank is calling his sister and can’t remember the first two digits of her phone number. He remembers the remaining five digits. What is the greatest number of attempts that Frank would have to make to complete the call? (He knows that the first digit of his sister’s phone number is not 0.)

60) A combination lock has a combination of 5 single digits, none of which are repeated. How many different combinations are there?

61) A pizza parlor provides customers with the opportunity to create their own single topping pizza by selecting from 4 different crusts, 5 different sauces, 3 different cheeses, and 15 different toppings. How many different pizzas with one topping are possible? If a second different topping choice is allowed, how many pizzas are possible?

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Permutations and Combinations

Classwork

62) What is the value of the following:

a. 6P2

b. 8P3

c. 10P2

d. 3P3

63) 30 dogs and their handlers enter a show ring. The judge will pick 5 dogs to place in the contest. How many different ways can the first, second, third, fourth, and fifth place be awarded?

64) a. You create a sundae with 3 out of 10 flavors at the Ice Cream Store. This is an

example of ____________.

b. You must fit 10 out of 15 dogs in the cages along the wall (one dog per cage). How many different ways are there to place them in the cages? This is an example of __________.

65) Find the value of the following:

a. 6C4

b. 5C1

c. 4C4

d. 6C2

66) There are 21 girls on a soccer team. Four of these girls will be picked to be on the All-American Team. How many different groups of players can be chosen?

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Homework

67) What is the value of the following:

a. 10P6

b. 9P4

c. 5P5

d. 4P1

68) 20 snowboarders enter a race. The top 4 will get medals. How many different ways can the first, second, third, and fourth medals be given?

69) a. You must buy 3 kinds of soda out of 8 at the store. This is an example of

__________.

b. Your parents inform you that you can only invite 30 people out of the 50 people that you wanted to invite to your party. The possibilities of the people you can invite is an example of ___________________.

70) Find the value of the following:

a. 10C8

b. 4C2

c. 6C5

d. 3C3

71) There are 20 children in a kindergarten class. Five of these children will be picked for the outstanding kindergarten award. How many different groups of kindergarteners can be chosen?

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Probability of Compound Events

Classwork

72) You are given a pair of dice. One die is numbered 1 through 6 but the other die is numbered 7 through 12. What are the odds of rolling a 3 and an 8?

73) A machine generates numbers randomly from balls numbered 5 through 15. Two numbers are selected, with replacement. What are the odds that both the numbers picked will be 8?

74) A bag with 6 blue marbles, 3 green marbles, and 4 orange marbles is lying on a table. What is the probability that John will pick 2 green marbles? (without replacement)

75) What is the probability that the first three cards drawn from a full deck of cards are clubs? (without replacement)

76) There are 6 male puppies and 3 female puppies. What is the probability that the first two puppies chosen will be males? (without replacement)

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Homework

77) What is the probability that the first three cards drawn from a full deck of cards are kings?

78) You dropped two coins. What is the probability that they will both land on heads?

79) Bill Gates wrote a computer program that generates three random numbers between 1 and 10. What is the probability that all three values will be three?

80) A lottery machine generates numbers randomly. Three numbers are picked between 1 and 20. What is the probability that all three numbers that are picked are 17?

81) There are 4 blue marbles and 2 red marbles. A marble is selected and not returned. What is the probability that two red marbles will be chosen?

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Probabilities of Mutually Exclusive and Overlapping Events

Classwork

82) Are these events mutually exclusive? Event A: Roll an even number on a six-sided number cube Event B: Roll a prime number on a six-sided number cube

83) Are these events mutually exclusive? Event A: Select a bird Event B: Select a bald eagle

Calculate:

84) P(selecting a queen or a 10) from a deck of cards

85) P(rolling a 2 or a 6) on a die

86) P(rolling a 2 or an even number) on a die

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Homework 87) Are these events mutually exclusive?

Event A: Roll a number greater than 2 on a six-sided number cube Event B: Roll a number less than 3 on a six-sided number cube

88) Are these events mutually exclusive? Event A: Select a consonant from the alphabet Event B: Select a vowel from the alphabet

Calculate:

89) P(choosing a 4 or a jack) from a deck of cards

90) P(rolling an odd number or a number greater than 3) on a die

91) P(choosing a club or a black card) from a deck of cards

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Complementary Events

Classwork

92) P(snow) = 20% P(no snow) =

93) P(A) = .9 P(not A) =

94) What is the probability of not selecting a queen from a deck of cards?

95) What is the probability of not rolling a 1 on a die?

96) What is the probability of not selecting a queen or a king from a full deck of cards?

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Homework

97) P(rain) = 5% P(no rain) =

98) P(A) = 3/5 P(not A) =

99) What is the probability of not selecting a four from a deck of cards?

100) What is the probability of not rolling a prime number on a die?

101) If 22% of the people in the room are bald, what percent are not bald?

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STATISTICS & PROBABILITY UNIT REVIEW

Statistics & Probability Multiple Choice Questions

Choose the correct answer for each question. No partial credit will be given. 1) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles.

What is the probability of selecting a black marble?

a. 7

4 b.

11

2

c. 4 d.

23

4

2) A bag contains 12 red marbles, 4 black marbles, 4 purple marbles and 2 pink marbles. What is the probability of selecting a white marble?

a. 7

4

b. 1 c. 0 d.

23

4

3) A die is rolled 8 times and a “5” is rolled three times. What is the experimental probability for rolling a 5?

a. 8

5 b.

8

3 c.

5

3

d. 1

4) Sam hits the baseball 15% of the time. If he swings the bat 40 times, how many hits

should he expect to make?

a. 6 b. 15 c. 20 d. 40 5) An ice cream stand has 15 flavors of ice cream, 3 types of syrup, and 10 different

toppings. How many different sundaes, consisting of one flavor of ice cream, one syrup, a nd one t op ping doe s t he st an d se rve?

a. 15 b. 45 c. 225 d. 450

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6) A town has all phone numbers begin with the same three digits, followed by 4 digits where repetition is allowed. How many different phone numbers are possible?

a. 7,200,000 b. 10,000 c. 720 d. none of these

7) Awards are given to the first, second and third place winners of a race in which 10

people participated. How many possible ways can the awards be given?

a. 6 b. 720 c. 10! d. none of these 8) Ted is choosing 4 songs from an album that contains 18 songs. How many possible

arrangements are there for Ted to create? a. 24 b. 3,060 c. 18! d. none of these 9) What is the probability of selecting two red cards from a deck of cards? (with

replacement)

a. 4

1 b.

2

1 c.

4

3 d. none of these

10) In a sample of 75 randomly selected students at a school, 32 are female. There are 1,371

students in the school. Using these results, predict the number of females in the school.

a. 275

b. 343

c. 585

d. 686

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11) The car dealership’s inventory is shown below

Sunrise Car Dealership

Car Make Number of Cars

Ford 550

Nissan 425

BMW 630

If a car is selected at random, what is the probability that the car selected is not a Ford or Nissan?

a. 0.26 b. 0.34 c. 0.39 d. 0.40

12) What is the probability of rolling a prime number or a number greater than 3 on a die?

a. 6

5 b.

3

2 c. 1 d. none of these

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Statistics & Probability Short Constructed Response Questions 13) Determine how many three-letter arrangements are possible with the letters

R , A , N , D , O , a n d M if no letter may be repeated. 14) What is the probability of rolling snake eyes on a pair of dice?

15) What is the probability of selecting a club and a heart from a deck of cards (without replacement)?

16) P(rain) = 10% ; P(no rain ) = ___________ 17) What is the probability of selecting a club or a jack from a deck of cards?

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Statistics & Probability Extended Constructed Response Questions Solve the problem, showing all work here in the packet. Partial credit may be given.

18) The amount of December snowfall, in inches, was recorded on the dot plots below. Use

the following dot plots to answer the questions below.

Snowfall – Oswego, NY x x x x x x x x x x x x x x x x x x x x x x x x x x 18 19 20 21 22 23 24 25 26 27 28

Snowfall – Fulton, NY

x x x x x x x x x x x x x x x x

24 25 26 27 28 29 30 31 32 33 34 a. What is the mean amount of snowfall in each town?

b. What is the difference of the means?

c. What is the mean absolute deviation of each of the data sets?

d. Which town has more variability in the amount of December snowfall?