Name Block Date Algebra 2- Semester 2 Review CALCULATOR ALLOWED Vocabulary: Biased sample Experiment Probability Census Favorable Outcomes Probability sample Cluster sample Hypothesis testing Randomized comparative experiment Convenience sample Inclusive Events Random Sample Complement Independent Events Sample Compound Event Joint Relative Frequency Sample Space Control group Margin of error Sample Event Controlled experiment Marginal Relative Frequency Simple Random Sample Conditional Probability Mutually Exclusive Events Standard Normal Value Conditional Relative Frequency Null hypothesis Statistic Dependent Events Observational study Stratified Sample Equally Likely Outcomes Outcome Systematic Sample Event Parameter Treatment Group Expected Value Population Variance 7.1 and 7.2 1. The door code to get into a top-secret laboratory is 6 digits. The first 3 digits of the code are all odd, the next three can be any digit. Digits can be used more than once. How many possible codes are there to gain access to this laboratory? What is the probability that all 6 digits are odd? 2. Ms. Ness decided to make a bunch of flags for Flag Day using four strips of colored paper. She placed one white (W), one red (R), one black (B), and one yellow (Y) strip of paper into a bag and randomly pulls out the strips one at a time, lining them up horizontally to create a flag like the one below. Using a capital letter to represent that colored strip, create the sample space of flags made by Ms. Ness. Then, use it to determine the following probabilities. a) She makes a flag with a red strip on top and a yellow strip on bottom b) She makes a flag with a white strip second or third 3. Carl and Pedro each put their names in a hat for a door prize. Two names will be selected, and there are a total of 40 names in the hat. What is the probability that Carl wins the first prize and Pedro wins the second?
4. The table shows the results of 75 tosses of a number cube. Find the experimental probability of rolling a 4. 1 2 3 4 5 6 10 12 16 15 9 13 7.3 5. A bag contains 11 beads- 2 blue, 3 yellow, and 6 red. Explain whether each event is independent or dependent. Then, calculate each probability. a) selecting a yellow, then a blue bead with replacement. b) selecting a yellow, then a blue bead without replacement. 6. The following table shows the results of a school-wide survey on the homecoming dance. Determine the probability of each event. Homecoming Dance Location Survey a) A student prefers the cafeteria Girls Boys Gymnasium 67 58 Cafeteria 53 37 b) A student prefers the cafeteria given that it s a girl. c) A surveyed student is male and prefers the gymnasium. d) Are the events prefers cafeteria and girl dependent or independent? Use probabilities to justify your answer. 7. The probability that a student slept at least eight hours the night before their final exam is 74%. The probability a student earns an A on the exam is 27%. The probability a student slept at least eight hours that night before the exam and earns an A on the exam is 20%. Are the events slept 8 hours and earned an A independent? Use probabilities to justify your answer.
7.4 8. Students and teachers at a school were polled to see if they were in favor of extending the parking lot into part of the athletic fields. The results of the poll are shown in the two-way table below. In Favor Not in Favor Students 16 23 Teachers 9 14 a) Create a table of the joint and marginal relative frequencies. Use your table to calculate the following probabilities: b) A randomly selected person was not in favor c) A randomly selected person was a student and in favor d) A randomly selected teacher was in favor 9. Sarah asked 40 randomly selected underclassmen at her high school whether they were planning to go to college and whether they were planning to move out of their parents or guardians homes right after high school. The results are summarized in the table below. Planning to Move Out Planning to Go to College Yes a) Create a table of the joint and marginal relative frequencies. No Yes 16 8 No 12 4 Use your table to calculate the following probabilities: b) A randomly selected person plans to go to college c) A randomly selected person was planning to move out and not go to college d) Which is more likely, that an underclassman planning to go to college is also planning to move out, or that an underclassman planning to move out is also planning to go to college? Justify your response with conditional probabilities.
10. The table shows the results of a customer satisfaction survey of 100 randomly selected shoppers at the mall who were asked if they would shop at an early time if the mall opened earlier. The results are shown in a table below. Ages 10 20 Ages 21 45 Ages 46 65 65 and Older Yes 13 2 8 24 No 25 10 15 3 a) Create a table of the joint and marginal relative frequencies. Use your table to calculate the following probabilities: b) A randomly selected person was not in favor c) A randomly selected person was between the ages of 46-65 d) A randomly selected person was between the ages of 46-65, given that they were not in favor e) Are the events between the ages of 46-65 and not in favor independent or dependent? Justify your response using probabilities. 7.5 11. A random table in the cafeteria is chosen. Sitting at the table is 2 freshmen, 5 sophomores, 7 juniors, and 2 seniors. A student is chosen at random from the table. What is the probability of choosing a freshmen or a senior? 12. The numbers 1 20 are written on cards and placed in a bag. Find each probability. a) choosing twenty or choosing an odd number. b) choosing a number less than ten or choosing a multiple of five.
13. In an apartment building with 50 residents, 16 of them have cats, 28 of them are students, and 9 of the students have cats. a) Make a two-way table and a Venn diagram to represent this situation. b) Use the table and/or diagram to find the following probabilities: a. A randomly selected resident is a student b. A resident is a student and has a cat c. A resident is a student or has a cat d. A resident does not have a cat 14. Men and Women at a gym were polled to see if they prefer the treadmill or the elliptical machine. The results of the poll are shown in the following Venn diagram: Men 28 25 Treadmill 38 44 a) What is the probability that a person at the gym prefers the treadmill? b) What is the probability that a randomly selected person at the gym is a woman? c) What is the probability that a randomly selected person at the gym is a man who prefers treadmills? d) What is the probability that a woman prefers the elliptical machine? e) Based on the results of the Venn diagram, are preferring an elliptical machine and being a male independent? Justify using answer using probability.
8.1 15. The average points per game scored by each NFL team during the 2006 regular season is listed below. 19.6 18.2 22.1 18.8 16.9 26.7 23.3 14.9 26.6 19.9 19.1 18.8 16.7 26.7 23.2 20.7 16.2 17.6 24.1 25.8 19.8 22.2 10.5 24.9 22.1 30.8 18.6 20.9 22.9 13.2 20.2 19.2 a) Determine the mean, median, mode, Q1, Q3, range, IQR, variance, and standard deviation. b) Make a boxplot for the data and sketch it below. c) Which measure for center and spread should be used to describe this data set? Why? d) Using the appropriate rule for determining outliers, identify any outliers. e) If there were outliers, how do they impact the measures you chose for center and spread? 16. The weights (in pounds) of dogs in a kennel are listed below. 10 21 37 41 106 50 65 57 45 38 45 27 12 24 a) Determine the mean, median, mode, Q1, Q3, range, IQR, variance, and standard deviation. b) Make a boxplot for the data and sketch it below. c) Which measure for center and spread should be used to describe this data set? Why? d) Using the appropriate rule for determining outliers, identify any outliers. e) If there were outliers, how do they impact the measures you chose for center and spread?
17. Given the following table, calculate the expected value of the raffle prize. Raffle Prizes Value $0 $5 $20 $200 Probability 0.76 0.16 0.06 0.02 8.2 18. Determine whether each survey is likely to represent the population. EXPLAIN. a) A survey asks the members of the math club whether math classes should be required for all four years of high school. b) Colorado State government sends out a survey to random Colorado City governments about the city s parking plans. 19. Determine whether each sampling method is likely to be biased. EXPLAIN. a. The principal at a school wants to know if new teachers feel that they have been given enough support from the administration. He makes appointments to interview half of the teachers who have been at the school for two years or less and ask for their feedback. b. A state politician s office is conducting a survey to find which issues are most important to the state s citizens. The office randomly selects 100 residents of the state s cities, 100 residents of the state s rural communities, and 100 of the state s suburban communities to call and ask to participate in a telephone poll. 20. In a survey of 100 town residents, 63 said they prefer the library s new hours. If you were able to survey all of the 23,000 town residents, how many would you expect to prefer the library s new hours? 8.3 21. Explain whether the following situation is an experiment or an observational study. A researcher compares incomes of people who live in rural areas with incomes of people who live in large cities.
22. Describe the treatment, the treatment group, and the control group of the randomized comparative experiment below. A researcher wants to know whether background noise affects people s abilities to complete simple cognitive tasks. She has the 20 people perform a series of tasks. Ten randomly selected subjects perform the tasks in a quiet room. The other 10 perform the tasks in a room traffic noise outside and muffled voices coming from the room next door. She records how successful each group of subjects is in completing the assigned tasks. 23. Explain whether the research question is best addressed through an experiment or an observational study. Then explain how you would set up the experiment or observational study. Does reducing the fat in a particular recipe make it less appealing? Will offering access to internet-equipped computers to non-members of a library increase the number of new members? 8.5 24. Determine whether the survey clearly projects the winner. Explain your response. A website had users vote for their favorite of three dog photos. 53% voted for photo 1 and 47% voted for photo 3. The margin of error is ± 9%. 25. Classify each sample as simple random, systematic, stratified, cluster, convenience, or self-selected. a) a store owner in the mall wants to determine whether a new brand of shoes will sell in her store. She surveys random people in the mall on the weekend. b) a city councilor wants to know how residents in the city will react to a new smoking policy. He surveys residents by mailing a random sample of voters in the city. c) the director of the student theater group wants to know which of three plays will have the largest student audience. He randomly chooses 20 freshmen, 20 sophomores, 20 juniors, and 20 seniors in the hall between classes.
26. The committee that is planning this year s prom wants to know what music to play at this year s prom. The committee suggests three different survey methods. Classify each sampling method. a) Survey every 10 th student in the school. b) Survey a list of students randomly selected from a computer. c) Survey the first 50 students that walk in the cafeteria. d) Which is most accurate? Which is least accurate? Explain. 8.7 z 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 Area 0.01 0.02 0.07 0.16 0.31 0.5 0.69 0.84 0.93 0.98 0.99 27. Scores on the Wechsler Adult Intelligence Scale (a standard "IQ" test) for the 20 to 34 age group are approximately normally distributed with a mean of 110 and a standard deviation of 25. Determine each of the following probabilities: a) that a randomly selected adult 20 34 scores below 135. b) that a randomly selected adult 20 34 scores above 160. c) that a randomly selected adult 20 34 scores between 97.5 and 172.5. d) that a randomly selected adult 20 34 scores below 72.5 or above 147.5. 28. Scores on a test are normally distributed with a mean of 78 and a standard deviation of 8. Determine each of the following probabilities: a) that a randomly selected student scored below 90. b) that a randomly selected student scored above 86. c) that a randomly selected student scored between 74 and 78. d) that a randomly selected student scored below 86 and above 90.
8.4 29. Below are the test grades for two different sections of AP Statistics on the same randomly picked chapter. 1st 66 88 98 97 91 98 96 103 88 98 92 100 70 93 70 81 86 89 87 Class 2nd Class 99 92 78 70 87 90 97 36 82 92 a) State the null hypothesis. b) Compare the results of the two groups. Does it appear that one class does significantly better in AP Stat than the other? 30. A company manufactures rubber balls. The company claims its product bounces twice as high as its leading competitor s product. In an experiment, bounce height is measured in feet. The results of seven trials are shown in the table. Company 3 3.5 3.2 3.6 2.5 4 3.9 Competitor 6 6.7 4.5 2.1 3.6 5.5 5.1 a) State the null hypothesis for the experiment. b) Compare the results of the two groups. Does it appear that the company s bouncy ball is significantly better than the other? 31. A cereal manufacturer sells boxes of cereal that list the weight as 20 oz., with standard deviation 0.67. A random sample of 60 boxes was weighed and a mean of 19.9 oz. resulted. Is there enough evidence to reject the manufacturer s claim?