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)336
C)694
D)729

Question

Quizplus · Accepted Answer

To find the score that places a student in the top 5% of all students taking the SAT, we look for the value that corresponds to the 95th percentile in a normal distribution with a mean (μ) of 515 and a standard deviation (σ) of 109. Using the Z-score formula or a standard normal distribution table, we find that the Z-score corresponding to the top 5% is approximately 1.645. Applying this to the SAT scores distribution: Z = (X - μ) / σ => X = Z*σ + μ => X = 1.645*109 + 515 ≈ 694.

Scores on the SAT Verbal Test in Recent Years Follow