2.2 Normal Distributions Date Period 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. Bobby's percentile. c. Calculator the z-score. e. Find Bobby's percentile by using the z-score and Table A from your book. f. Find Bobby's percentile by using the normaica'f fu nction 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 ofthe (unshaded). the z-score. region shaded to the right of Amy's :- score. e. Use a graphing utility to find the c. Calculator the z-score. 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. 3. 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