2. Areas under the normal curve The following figure shows the normal distributi
ID: 3196223 • Letter: 2
Question
2. Areas under the normal curve 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 te standard normal distribution is located below z-score values less than the mean (p) 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 heip 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 mainExplanation / Answer
mean = 259
std. dev. = 33
259 - 33 = 226 i.e 1-sigma
259 + 33 = 292 i.e. 1-sigma
A score of 226 is 1-sigma below the mean while a score of 292 is 1-sigma above the mean. This means that the percentage of male students with score between 226 and 292 is (34.13*2) = 68.26
325 - 259 = 66 (i.e. 33*2 i.e. 2-sigma)
A score of 325 is 2 sigma above the mean. As a result, the percentage of male students socres below 325 is (50 + 34.13 + 13.59) = 97.72
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