Answer to Question #217748 in Statistics and Probability for Ahmad

Question

The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?

Answer 1

The mean of normal distribution$=1500$

The standard deviation of normal distribution$=300$

The results of students who score in the top ten percent of this test have results:

$mean+\left(z\times \sigma \right)$ ,

Where

$\:\sigma =standard\:deviation$

$z$ ​is obtained from z- tables to be :$z=1.281552$

The minimum score that will qualify for the scholarship will be:

$Minimum\:score=mean+\left(z\times \sigma \right)$

$Minimum\:score=1500+\left(1.281552\times 300\right)$

$Minimum\:score=1884.4656\approx 1884$

Therefore the minimum score is $1884$ .