Question #24974

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?

Expert's answer

We have a normal distribution with a mean of 1500 and a standard deviation of 300.

students who score in the top 10 percent of this test have results:

p ( x>mean+z*sigma ) = 0.1

p - probability,

sigma - standard deviation.

From the tables:

z = 1.281552.

Therefore, the minimum score that qualifies for the scholarship:

min = mean+z*sigma = 1500 + 1.281552*300 = 1884.4656 ~ 1884.5

Answer:& the minimum score equals 1884.5

students who score in the top 10 percent of this test have results:

p ( x>mean+z*sigma ) = 0.1

p - probability,

sigma - standard deviation.

From the tables:

z = 1.281552.

Therefore, the minimum score that qualifies for the scholarship:

min = mean+z*sigma = 1500 + 1.281552*300 = 1884.4656 ~ 1884.5

Answer:& the minimum score equals 1884.5

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