Attempts Average: /6 6. Area under the normal distribution Aa Aa The folowing fi

Question

Attempts Average: /6 6. Area under the normal distribution Aa Aa The folowing 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 proporton on each side. 0.13%, depicts the remaining area under the arve. 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 (+3a). Also, because the normal distribution is symmetrical. 0.13% of the area under the standard normal distribution is located below z-score vaues ess 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 nationwi ubjects: mathematics, reading, writing, science, the arts, civics, economics NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12 de assessment of students' proficiency in nine civics, economics, geography, and U.S. history. The main In 1994, the U.S. history male these scores are normally distributed with the given mean and standard deviation. scores for male students had a mean of 259 with a standard deviation of 33. Assume that A score of 160 is below the mean, while a score of 358 is above the mean. This means that the percentage of male students with scores botween 160 and 358 is A score of 292 is above the mean. As a result, the percentage of male students with

Explanation / Answer

as we know that z score =(X-mean)/std deviaiton

hence

a score of 160 is 3 standard deviation below the mean ; while a score of 358 is 3 standard deviaiton above the mean. this means that the percentage of students with scores between 160 and 358 is

99.74%

a score of 292 is 1 stanard deviaiton abvoe the mean . as a result the % of male students with scores below 292 is 84.13%

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