6-16. Most students will find that Myriah does the dishes between 8 and 17 of the 30 days, or about 2 to 4 days per week.

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1 Lesson If the nickel is tossed and the die rolled there are 2 equall likel outcomes. He can make a list of each of the possible outcomes, assign one plaer to each outcome (H-Juan, H2-Rolf, T6-Jordan), and then toss the coin and roll the die to select a: 5%. See the table at right. b: = 75% 6-7. a: preface b: biased wording c: desire to please d: fair question 6-8. Less than 0; Possible justifications: log() = 0, so log (0.3) is less than 0. On the graph of = log(), the -values are negative for all < a: cm 3 b: 0.04 g/cm The intersect at ( 2,0) and (3, 0). Large Backard? 6-. Possible answer would be a sphere for the head and clinders or cones for the legs. es 0.75 Garage? es 0.80 no no Lesson Most students will find that Mriah does the dishes between 8 and 7 of the 30 das, or about 2 to 4 das per week Theoretical probabilit: P(sum 6) = ; 0.42(7) 3 das a week c: Possible answer: Research: What is the average commute distance to school for teenagers? Surve: What is the distance from where ou live to school? 6-9. a: = 2 b: an number ecept 0 c: = Students will need to solve graphicall to get a: 3 < < 3 b: 2 < < c: 2 or f 3 () = 2 ; See graph at right. f() f - () 205 CPM Educational Program. All rights reserved.

2 Lesson b: Theoreticall, the series should last for games, so 6 games b: Theoreticall, a streak of 4 or more has probabilit of about 48%, a streak of five or more about 25%, a streak of si or more 2%, and a streak of seven or more about 6% a: See diagram at right. b: In the RR rectangle, 8 38 i 8 38 = %. R B G c: Add the RR, BR, and GR rectangles, %. R d: Considering onl the column in which the second spin is red (RR, BR, GR), the probabilit the first spin is red (RR) is %. B G e: The are the same The surve is not random. The sample is mostl adults who ma work in the same or similar fields. People ma be influenced b the responses of others. An individual ma have several favorites but onl state one It is the log 5 () graph shifted 2 units to the right. See graph at right a: b: ( ±6, 2 ) 205 CPM Educational Program. All rights reserved. Core Connections Integrated III

3 - Lesson a: 7.83% b: 5% and % c: About 7.8% ± 3% def. flashlights b: Theoreticall, there will be 7.39 streaks of three or more in 60 das Each uses a convenience sample. Each sample comes from a distinct population with people who have man things in common, including attitudes and beliefs about the subject matter of murals See table at right = 30% a: = 2 b: = es c: 2 = log.75 () d: 7 = log (3) 6-4. a: = 0 2 b: She should multipl b ( 2). = 7 Second Jar ellow 0.30 orange 0.50 black 0.60 First Jar purple white CPM Educational Program. All rights reserved.

4 Lesson a: 0.56 and 0.74 b: 65% ± 9% Answers will var, but should be 3% plus/minus a number smaller than.7% a: feet b: cm c: meters Students should conclude that energ usage will change b.3% to.7%. Indiana could save up to $.7 million, but could end up spending $5.3 million a: Answers will var. Like a tournament, the students could be paired and the coin tossed for each pair. The winners are paired and the coin tossed again, repeating until there is just one student. b: Three tosses. Tossing a coin 3 times has 8 equall likel outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Assign each student an outcome and toss the coin 3 times. c: Yes. Use the method outlined in part (b) repeatedl until a baseball plaer is not selected a:.204 b:.63 c: = 6 d: a: < < 3 b: or CPM Educational Program. All rights reserved. Core Connections Integrated III

5 Lesson a: 6 or 6.25%; es b: Her stud provides no reliable evidence of her conclusion. She uses a convenience sample of onl four people. Her question introduces bias with the preface about violence and crime. There ma also have been a desire to please the interviewer. She uses a closed question, forcing romantic comedies as the onl alternative to action movies. Even if there is no real preference among moviegoers, it is plausible that four people will have the same opinion between an two tpes of movies sample mean: 248, upper bound: 25037, lower bound: 24587; 90% of the time we epect that the cop machine will need maintenance after 248 ± 225 copies. The interval of confidence is from to copies is within the interval of confidence, so the research compan ma support the cop machine compan s claim. The ma also state that the cop machine compan is pushing the limits with a claim of at least copies a: 0.2 b: A difference of zero is not within the margin of error, so it is not a plausible result. A difference of zero means that there is no difference in the percentage of food removed with detergent compared with the percentage of food cleaned off with plain water. c: Yes. Because a difference of zero is not within the margin of error; a difference of zero is not a plausible result for the population of all food cleaned. We are convinced there is between 3.5% and 20.5% (2% ± 8.5%) more food removed with detergent than with plain water a: Yes. Possible response: Both equations have the same solutions. b: Yes. Possible response: Both equations have the same solutions a: = 6.5 b: = 3.75 or = a: = 7 b: = c: (2, 5) and (, 4) d: 7 2, 7 2 ( ) and( 2 3, 2 ) 205 CPM Educational Program. All rights reserved.

6 Lesson The first process is wildl out of control; sstems wildl out of control are often caused b ineperienced operators. The second process is full in control. The third process is technicall out of control at onl one point, but the cclical nature of the process is disconcerting. An hpothesis that eplains wh the process is cclical over 20 hours is acceptable Yes, 20% is within the margin of error of 3% ± 0% Yes. As little as.75 ounces is still within specifications a: See diagram at right. b: = % Mom Jazz Reggae Wedding c: 2 i i 2 = % d: P(dadandemoticon) P(emoticon) = 4 3 = 3 4 = 75% Dad See graph at right. = log( 6) a: W () b: No; when the points are interchanged, the input = 0 has two outputs Assuming a normal distribution, normalcdf(68, 75, 63.8, 3.8) 3% of U.S. women fall between 5' 8" and 6' 3" tall. Therefore, 87% of U.S. women are shorter or taller than the height range of the cockpit. 205 CPM Educational Program. All rights reserved. Core Connections Integrated III

7 Lesson 6.3. Da This is a Gambler s Ruin problem. The plaer with more coins alwas has a better chance of winning in the long run. Theoreticall, P(Jill) = %, P(Jack) = % a: Before asking the question, the person conducting the surve is connecting funding decisions to censorship. b: People at home during the da are more likel to have time to bake than the general population. c: Possibl health habits. Health habits might increase the number of apples ou eat and also decrease the number of cavities ou have. The apples are not preventing the cavities, the health habits are a: 24 = b a b: 7 = (2) 3 c: 5 = log 2 (3) d: 6 = log 2q (4p) a: undefined b: 7 c: f() f () = + 6. Students can justif using a table, a graph, or b substituting a value = 5 ( 9.69 is etraneous) a: (4, 8, 4 3 ), (5, 0, 5 3 ) b: For this sequence, if the short leg is n units long, then the long leg is n 3 units long, and the hpotenuse is 2n units long. 205 CPM Educational Program. All rights reserved.

8 Lesson 6.3. Da a: 0.0 b: i. 25% of % of 40 = 6 putts go into the hole ii. to 6 will represent a putt that goes into the hole; 7 to 80 will represent a putt that misses. c: A difference of zero means that there is no difference between the proportion of putts that go in the hole with the new club and the proportion of putts that go in with the old club. A difference of zero is within the margin of error, so it is a plausible result. d: No. A difference of zero is within the margin of error, and a difference of zero is a plausible result for the population of all putts. We are not convinced there is a true difference in the number of putts that go in with the new club compared to the old club. Event A 6-8. a: See possible diagram and answers below. Yes No Cell A is the proportion of times the sstem correctl activated the alarm. Cell B is the proportion of times the alarm was correctl not activated. Cell C is the proportion of times A happened and the alarm was incorrectl not activated. Cell D is the proportion of times A did not happen and the alarm was activated. Or as a tree diagram: b: = 97.6% c: Yes, it is independent because the accurac of the alarm is the same regardless of whether event A occurs or not. Detection Sstem Event A Not Event A Correct Incorrect correct incorrect correct A C B D Answers var but students should recognize that 0 < b < = f () = ( ) for ; See graph at right a: $40, b: 24.2 ears c: $64, incorrect CPM Educational Program. All rights reserved. Core Connections Integrated III

9 6-86. a: See graph at right. b: Answers will var. See graph at right. Using statistical computations, we find that the boundaries are $6.7 and $3.29. c: Answers will var. normalcdf(6.7, 3.29, 0, 2) CPM Educational Program. All rights reserved.