Question

1. Properties of the normal curve 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 2003, the mathematics scores for male students had a mean of 278 with a standard deviation of 37. 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. O A quarter of the total area under the curve is above 278. The curve is bell shaped, with a single peak over 278. The two ends of the curve approach the horizontal axis but never touch it. One-half of the total area under the curve is above 278. One-tenth of the total area under the curve is below 278. One-half of the total area under the curve is below 278. above the mean. The value 167 is Therefore, below the mean, and the value 389 is of the male students have scores between 167 and 389.

Answer 1

Given X: mathematic's scores of male students. Xa Nlm = 278 6=37) The Curve is bell shaped, with single Peak over 278. The Two ends of the curre approaches the horizontal axis but never touch it .. one half of the total aree under the cune is above 278 one held of the total area under the Curie is below 278. Using Empirical Rule rerbell shaped distribution 167 = le-36278-3437 389 e + 38 = 278+ 3x37 Hence The vame 167 is 3 standard deviation below the mean, and the raue 389 is 3 standard deviation above the mean, Therefore gg. 77. ol male students have sceses between 167 and 389. one half Curre of the total is below 278. area under the