3. Properties of the normal curve Aa Aa The National Assessment of Educational P

Question

3. Properties of the normal curve Aa Aa The National Assessment of Educational Progress (NAEP) conducts 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 2000, the science scores for female students had a mean of 146 with a standard deviation of 35. Assume that these scores are normally distributed with the given mean and standard deviation. Which of the following are properties of the normal curve representing the distribution of the scores? Check all that apply. The two ends of the curve approach the horizontal axis but never touch it. The curve is symmetrical about a vertical line through 146. One-half of the total area under the curve is below 146. A quarter of the total area under the curve is above 146. The curve is symmetrical about a vertical line through 216. One-half of the total area under the curve is above 146 The value 41 is below the mean, and the value 251 is above the mean. Therefore of the female students have scores between 41 and 251.

Explanation / Answer

correct options are 1,2,3 and 6

the two ends of the curve approach.............

the curve is symmetrical........

one half of the total area under the curve is below 146

one half of the total area under the curve is above 146

the value 41 is 3 standard deviation below the mean , and the value 251 is 3 standard deviation above the mean.

Therefore 99.73% of the female students have score between 41 and 251.

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