Question

6. Area under the normal distribution The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (u) plus three standard deviations (+30). Also, because the normal distribution is symmetrical, 0.13% of the area under the standard normal distribution is located below z-score values less than the mean (u) minus three standard deviations (-30). 34.13% 34.13% 13.59% 13.59% 2.15% 2.15% 0.13% 0.13% Use the figure to help you answer the following questions. The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students' proficiency in nine subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12. In 1994, the U.S. history scores for male students had a mean of 259 with a standard deviation of 33. Assume that these scores are normally distributed with the given mean and standard deviation. A score of 226 is below the mean, while a score of 292 is above the mean. This means that the percentage of male students with scores between 226 and 292 is above the mean. As a result, the percentage of male students with A score of 325 is scores helow 325 is

Answer 1

A score od 226 is 1 standard dev below the mean and 292 is 1 standard dev above the mean. % of students between is 68.28%

A score of 325 is 2 sd above mean. % below 325 is 50+34.13+13.56 = 97.69%

99.87% students have score above = 259-3*33 = 160