Question

The SAT and ACT college entrance exams are taken by thousands of students each year. The mathematics portions of each of these exams produce scores that are approximately normally distributed. In recent years, SAT mathematics exam scores have averaged 480 with standard deviation 100. The average and standard deviation for ACT mathematics scores are 18 and 6, respectively. (a) An engineering school sets 560 as the minimum SAT math score for new students. What percentage of students will score below 560 in a typical year

Answer 1

78.814%

Explanation:

mean, = 480 points.

standard deviation, σ = 100 points.

If 560 is the minimum score, x = 560. We want the % of students who will score BELOW that. Use the formula for z-scores:
`z = (x-u)/(standard deviation)` to get the z score: (560-480)/(100) = 0.8.

Using a z-score table: the value under 0.8 is 78.814%.