FSA 7 th Grade Math. MAFS.7.SP.1.1 & MAFS.7.SP.1.2 Level 2. MAFS.7.SP.1.1 & MAFS.7.SP.1.2 Level 2. MAFS.7.SP.1.1 & MAFS.7.SP.1.

Transcription

1 FSA 7 th Grade Math Statistics and Probability Two students are taking surveys to find out if people will vote to fund the building of a new city park on election day. Levonia asks 20 parents of her friends. Quenton asks every other person leaving the library until he has asked 20 people. Ruth calls 20 randomly-selected registered voters. Vince sends s to 20 friends. Which sample will be the most representative? Give reasons for your answer. There are 3,000 people in a travel club. A random sample of 50 of the people in the club found that 12 people like mountain vacations best. Select statements that are supported by the sample data. Circle all that apply. A. About one-uarter of the people sampled like mountain vacations best. B. About 12% of the people in the travel club like mountain vacations best. C. Fewer than 500 people in the entire travel club would likely say they enjoy mountain vacations best. D. An estimated 720 people in the travel club like mountain vacations best. E. More than 2,000 people in the travel club would likely say they prefer other vacations over mountain vacations. A jar contains 1,000 marbles. Omar is entering a contest to guess the number of any one color of marbles in the jar. He is allowed to take four random samples of 200 marbles, and his results are shown in the table. Which statements are true? Choose all that apply. A) The total number of red marbles in the jar is approximately 168. B) There are likely more blue marbles in the jar than any other color. C) There are probably more white marbles than green marbles in the jar. D) The number of green marbles in the jar is approximately 21% to 33% of the marbles in the jar. E) The ratio of the number of red marbles in the jar to the number of green marbles in the jar is most likely greater than the ratio of the number of white marbles in the jar to the number of blue marbles in the jar.

2 Jackson uses a random number generator to choose 20 students from each grade and asks how long they spend on homework. Niko says that Jackson s sample is biased. A) Do you agree with Niko? Explain. B) If it is biased, identify a different 60-student sample that can be chosen to better represent the school population. Jackson s School Grade Students Write a sentence comparing the medians of the two data sets? Describe the center and interuartile range of the data sets and what those measures mean for the lengths of rock and jazz songs. Ms. Lane teaches two sections of a math class. Below are the results of a pop uiz she gave each section. Which section s data shows the most variability? A. Section B; the maximum number of students scored 9 B. Section A; the maximum number of students scored 6 C. Section B; students in this section scored between 1 and 9 D. Section A; students in this section scored between 1 and 10 The data shows the tree heights in feet in parks in different parts of a city. Circle a statement that describes the height data. Select all that apply. A. Trees in the north-side parks are, on average, taller. B. The mean absolute deviations are 5.25 feet for the south-side tree data and 4.5 feet for the north-side tree data. C. The interuartile range is greater for the north-side tree data. D. The data sets have an almost complete overlap. E. The means are the same, but the medians are different.

3 Which of the following numbers could represent the probability of an event? A. -1 B. 2.4 C. 0.4 D E. 0 F G Probability of an Event? Yes No Draw a line from each probability to the word or phrase that best describe the probability , % Certain Eually Likely Impossible Likely Unlikely Determine if each statement is True or False for each statement about the spinners. Justify your answers. A) The probability of spinning a triangle is the same on both spinners. B) The probability of spinning a suare is greater on Spinner B than Spinner A. Peter will use a random number generator 1,200 times. Each result will be a digit from 1 to 6. Which statement best predicts how many times the digit 5 will appear among the 1,200 results? A) It will appear exactly 200 times. B) It will appear close to 200 times but probably not exactly 200 times. C) It will appear exactly 240 times. D) It will appear close to 240 times but probably not exactly 240 times. A bag contains blue, red, and green marbles. Paola draws a marble from the bag, records its color and puts the marble back into the bag. Then she repeats the process. The table shows the results of her experiment. Color Number of Times Drawn Blue 14 Red 30 Green 6 Part A) Using her results predict the probability that she will pull a green marble from the bag. Part B) If she repeats the experiment 200 times, how many times would you predict that she would pull a blue marble?

4 Coach Nelson used the spinner to determine which five warm-up exercises the team will do at the start of practice on Monday, Wednesday, and Friday. She recorded the results in this table. A. Based on her results, what was the experimental probability of spinning a Push-up? B. How does the theoretical probability of spinning each exercise compare to the experimental probability in Coach Nelson s experiment? Justify your answer. Marcus rolled a number cube 50 times and recorded the number of times he rolled an even number. Staci rolled a number cube 100 times and recorded the number of times she rolled an even number. Jamil rolled a number cube 300 times and recorded the number of times he rolled an even number. Whose experimental probability should have been closer to the theoretical probability and why? The spinner face shown is divided into 8 sections. The arrow on this spinner is spun once. What is the probability that the arrow will land on a section labeled with a number less than 4? A) & ' B) ( ' C) & ) D) ( ) You can buy popcorn at the Village Theatre in small, medium, or large sizes. The popcorn can be buttered or plain. List all possible outcomes. In 25% of the basketball games Kevin plays, he makes exactly 2 baskets. What is the experimental probability that Kevin will make exactly 2 baskets in each of the next 15 games he plays? Which simulation could not be used to find the probability? A) Place four slips of paper in a bag with one marked makes exactly 2 baskets and 3 marked not exactly 2. Pull a slip 15 times, replacing the slip after each pull. B) Use a spinner with 4 eual sections and designate one of the sections to represent makes exactly 2 baskets. Spin the spinner 15 times. C) Use a coin and let heads represent makes exactly 2 baskets. Flip the coin 15 times. D) Use two coins and let both landing with heads up represent makes exactly 2 baskets. Flip the coins 15 times.

5 Shawna makes a hit 30% of the time that she is at bat. Select the model that could be used to simulate the experimental probability that Shawna will make a hit the next 20 times she is at bat. For each, assume the simulation is performed 20 times. Circle all that apply. A. Rolling two number cubes with 1 6 on them and counting the times two 5s are rolled B. Having a bag with the digits 0 9 written on individual slips of paper and counting the times7, 8, or 9 is drawn C. Using a spinner divided into 3 congruent sections, one labeled hit, and counting the times the spinner lands on hit D. Having 10 index cards, 3 of which are red, and counting the times when a red card is randomly selected from the stack. E. Having a bag with 20 marbles, 6 of which are white, and counting the times when a white marble is randomly drawn from the bag A number cube has the numbers 1 6 written on its sides. The number cube is rolled 300 times. Place a check mark in the box next to each likely prediction. A. A 4 would be rolled about 50 times. B. A 6 would be rolled about 50 times. C. A 3 would be rolled about 10 times. D. The result would be an even number about 50 times. E. The result would be an even number about 150 times. F. The result would be greater than 4 about 150 times. Describe an event involving a number cube for which the experimental probability and theoretical probability not eual? Explain why the values could differ? Heidi spins the spinner shown. She records her results in the line plot. A) Find the theoretical probability of spinning a 2? B) Find the experimental probability of spinning a 2? C) Compare the results for A and B. Why are the results different or the same?

6 40% of blood donors have Type A blood. Consider the following simulations: Simulation A - 5 marbles in a bag, 2 blue and 3 red with blue representing Type A Simulation B Use a die with one and two being Type A Compare the simulations, which one would be best to find the probability that it will take at least 4 donors to find one with Type A blood? : The registered voters in Ruth s sample are the most representative. Sample reasoning: Levonia s sample ignores people without children. Quenton s sample includes only library users. Vince s sample includes only his friends. Also, the other samples may include nonregistered voters who will not be able to vote for the new city park funding. : D : A, D, E : 100 : B, D, E : A) Yes, because there are twice as many 6th grade students as there are 7th or 8th grade students. B) He could use the random number generator to randomly choose 30 students from 6th grade, 15 students from 7th grade, and 15 students from 8th Grade. : The median of the teenagers that saw a movie last summer was 5 times the median of the adults that watched a movie last year. : The jazz tunes have a greater median length and a greater interuartile range. So, the jazz tunes are generally longer, and there is more variability in their lengths. : D : A, B, D : : A) No B) No C) Yes D) Yes E) Yes F) Yes G) No : ¼ Unlikely; 0.0 Impossible; 5/10 Eually Likely; 100% Certain; 75/100 Likely : B : a) True because the likelihood of spinning a triangle with spinner A is ¼ and with spinner B is 2/8. b) False because the likelihood of a spinning a suare with spinner B is 3/8 and with spinner A is ½.

7 : B : Part A) 0.12 Part B) 0.12(200) = 24 : 0.34 : 2/15; The theoretical probability of spinning each exercise is 1/5. The theoretical probability of spinning a push-up is less than the experimental probability. : Jami s experimental should be closer to the theoretical since he had a greater number of trails. : ¾ : small buttered, small plain, medium buttered, medium plain, large buttered, large plain : C : B,D,E : A, B, E : B : : Answer may vary. One example: The theoretical probability of rolling a 2 is 1/6. Ana rolls the dice 20 times and 2 is a result five times. Ana s experimental probability is ¼. The theoretical probability is what should happen while the experimental probability is what actually happened. More trials should give results closer to the theoretical probability. : A) 1/5 B) ¼ C) The experimental probability is greater than the theoretical probability because the theoretical probability is what should have happened while the experimental probability is what id happen. : Simulation A because 2 out of 5 is 40%. Simulation B does not give the correct percent.