Question

Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution. How high must a student score in order to place in the top 5% of all students taking the SAT?

a) 301
b) 694
c) 336
d) 729

Answer 1

To place in the top 5% of all students taking the SAT, a student must score approximately 694. Among the given answer choices, the correct option is b) 694.

Step-by-step explanation:

To determine how high a student must score in order to place in the top 5% of all students taking the SAT, we can use the standard normal distribution. Given that the scores on the SAT verbal test follow approximately the N(515, 109) distribution, we need to find the score value that corresponds to the 95th percentile. The 95th percentile corresponds to a z-score of approximately 1.645. We can use the formula z = (x - mean) / standard deviation to find the corresponding score value. Rearranging the formula, x = z * standard deviation + mean, we get x = 1.645 * 109 + 515 ≈ 694.

Therefore, a student must score approximately 694 in order to place in the top 5% of all students taking the SAT. Among the given answer choices, the correct option is b) 694.