For the questions below, assume the populations are normally distributed. 1. Bobby earned a score of 378 on the CST math Geometry test. He finds out from his school that the mean score is 350 with a standard deviation of 50. Bobby wants to know how well he did on the CST compared to his peers. a. Draw a Normal curve for the data. b. Use the Normal curve to estimate d. Use the Normal curve to estimate the z-score. c. Calculator the z-score. Bobby's percentile. e. Find Bobby's percentile by using the z-score and Table A from your book. f. Find Bobby's percentile by using the normalcdf function Of your graphing utitlity. 2. Amy took the SAT math and scored a 652. The mean score on the SAT math is 580 with a standard deviation of 100. What percent of students score higher than Amy on the SAT math? a. Draw a Normal curve for the data b. Use the Normal curve to estimate d. Use Table A to find the area of the (unshaded). the z-score. c. Calculator the z-score. region shaded to the right Of Amy's z- score. e. Use a graphing utility to find the area Of the region shaded to the right of Amy's score. 3. Tabitha is studying concentrations of a fertilizer in local rivers and lakes. The average level of fertilizer is 50 ppm with a standard deviation of 6 ppm. She tests a sample from the delta and finds it to contain 40 ppm of fertilizer. a. Draw a Normal curve for the data b. What percent of rivers and lakes c. What percent have a higher ppm (unshaded). have a lower ppm than the sample? than the sample? dec. percent = normalcdf(a , b, 'l, o) a = lower bound, h = upper bound, = pop mean, = pop St. dev 4. The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. a. Draw a Normal curve for the data b. What percent of students in the (unshaded). c. What percent Of student have a GPA below 2.0? course have a GPA between 2.9 and 3.8? 5. The average age Of a group Of fans at a hockey game is 34 years with a standard deviation Of 8 years. a. Draw a Normal curve for the data (unshaded). b. What percent Of fans are between c. What percent Of fans are Older 18 and 27 years Old? than 50 years Old? 6. The average score on the Chapter 1 Stats test was 81 with a standard deviation of 7. a. If you were in the 50th percentile, what was your Score on the test? b. If you were in the 84th percentile, what was your score on the test? c. If you were in the 70th percentile, what was your score on the test? 7. The average points scored by high school football teams in your region is 24 points with a standard deviation of 9 points. a. If your team is in the 50th percentile, how many points does your team average a game? z score AP Statistics 2.1 Transformations b. How many points per game does a team average with a z-score of -1? dec. percent = normalcd/(a, b, 'l, CT) a = lower bound, b = upper bound, Investigative Task c. How many points per game does a team average with a z-score of 1.6? pop mean, a = pop sr. dev Name Date Task A: The data set below shows the temperatures for the last 20 days in Tracy CA at noon (F). 98 101 102 101 87 92 85 95 92 105 94 107 97 105 97 90 85 84 Period 100 82 l. Describe the Distribution Of the Data: 2. It was discovered that the thermal sensor used was not calibrated correctly and was Off by 6 degrees such that the first temperature above (98) should have really been 92. Adjust all the temperatures to the new calibration. 3. Pages 92-98 discuss a variety of transformations we can perform on data, What kind is this? 4. Describe the Distribution Of the Data after you have completed the transformation. 5. What do you notice about the change in SOCS? 6. Create a general rule with respects to SOCS what changes and what doesn't change when we perform this type of transformation on a data set? Do you think this will always be true? Task B: The data set below shows the length Of 19 randomly selected pine beetles collected in Yosemite (in). 3.1 1.9 2.4 2.7 1.6 2.6 2.9 2.5 2.6 2.5 0.8 2.3 3.2 2.2 3.1 3.0 2.6 2.9 l. Describe the Distribution of the Data: 2. The researcher just realized they need to submit their findings in metric units. There are every inch. Convert the data set into cm for them, 3. Pages 92-98 discuss a variety of transformations we can perform on data. What kind is this? 1.7 cm in 4. Describe the Distribution of the Data after you have completed the transformation. 5. What do you notice about the change in SOCS? 6. Create a general rule with respects to SOCS what changes and what doesn 't change when we perform this type of transformation on a data set? Do you think this will always be true?