In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation
Of 200, what is the lowest possible score a student needs to qualify for acceptance into
The university?
A) 1250
B) 1100
C) 1330
D) 1400

Question

Quizplus · Accepted Answer

To find the lowest possible score to be in the top 5%, we use the z-score formula for the 95th percentile, since the top 5% would start from the 95th percentile upwards. The z-score for the 95th percentile is approximately 1.645. Using the z-score formula: Z = (X - μ) / σ, where Z is the z-score, X is the score, μ is the mean, and σ is the standard deviation, we can solve for X: 1.645 = (X - 1000) / 200. Solving for X gives us X = 1.645 * 200 + 1000 = 329 + 1000 = 1329. Since test scores are whole numbers, rounding up gives us 1330 as the lowest possible score to be in the top 5%.

In Order to Be Accepted into a Certain Top University