Activity 9: 14.4 B comparing scores and Percentiles Name: Recently, different midterm tests were given in each of two sections. Since the school has large class sizes, the test scores in both sections are approximately normally distributed. In Barney's section, the mean was 80 and his score was 90. In Wilma's section, the mean was 71 and her score was 83. Is it possible to determine who did better? The absolute comparison of the test scores does not tell you how well each did with respect to the other students in the class. So let's use Statkey https://www.lock5stat.com/StatKey/ to help us determine an answer to this question. 1. Determine the percentage of students in Barney's class that scored below Barney's grade of 90. Recall that the mean for his class was 80. The standard deviation of the test scores in Barney's section was 6.7. (round to the nearest whole number percent) 2. Determine the percentage of students in Wilma's class that scored below Wilma's grade of 83. The standard deviation of test scores in Wilma's section 6.1. Recall that the mean was 71. _ (round to the nearest whole number percent) 3. Who did batter, Barney or Wilma? Explain. 4. Determine the percentage of students in Barney's class that failed the test, that is, received a grade below 65? Recall that the mean for his class was 80. The standard deviation of the test scores in Barney's section was 6.7 .. nearest whole number percent) (round to the Percentiles: Use Statkey Suppose you want to know how you stand among all the students in your class who took the midterm test. We can use percentiles to help us. A percentile is the percentage of test scores that are less than a given x-score. That is, the percentile corresponding to an x-score is the area under the normal curve to the left of the x-score. For example, Barney's classmate received an 84 on the midterm test. The percentage of students who received a grade less than 84 is the classmate's percentile, or relative position, in the class. This percentage is represented by the following shaded area. 60 65 70 75 80 85 90 95 100 5. Calculate the percentile for the student who scored an 84 Recall that the mean for his class was 80. The standard deviation of the test scores in Barney's section was 6.7( round to the nearest percent) 6. Another student in Barney's class received a grade of 75. What is his percentile? (round to the nearest percent) 7. In a national survey, it was determined that the number of hours high school students watch television per year is approximately normally distributed. If the mean is 1500 hours, and the standard deviation is 100 hours. a. If a high school student watches 1650 hours a year, what percentile is this student in? (round to the nearest percent). b. If a student is in the 80th percentile, how many hours a year does this student watch? This one is challenging! Round to the nearest hour.