High School

What score must a learner earn on the SAT mathematics test in order for the score to be at the 89.97th percentile? Round up to the nearest whole number.


Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.


Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:


For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.

For the SAT critical reading score, the mean was 501 with a standard deviation of 112.

For the SAT mathematics score, the mean was 516 with a standard deviation of 116

A. 631

b. 670

c. 642

d. 665

What score must a learner earn on the SAT mathematics test in order for the score to be at the 89 97th percentile Round up

Answer :

The score a learner must earn on the SAT mathematics test to be at the 89.97th percentile is approximately 643. Option C

How to find the What score must a learner earn on the SAT mathematics test in order for the score to be at the 89.97th percentile

To find the score that corresponds to the 89.97th percentile on the SAT mathematics test, we need to use the given mean and standard deviation.

Given:

Mean (μ) = 516

Standard Deviation (σ) = 116

Percentile = 89.97th

We need to find the score (x) that corresponds to this percentile.

Using a standard normal distribution table or a statistical calculator, we can find the z-score that corresponds to the 89.97th percentile. The z-score represents the number of standard deviations away from the mean.

Using the z-score formula:

z = (x - μ) / σ

We rearrange the formula to solve for x:

x = z * σ + μ

Let's calculate the z-score:

z = invNorm(0.8997) [Using a statistical calculator or table]

z ≈ 1.28

Now, substitute the values into the formula:

x = 1.28 * 116 + 516

x ≈ 642.48

Since we need to round up to the nearest whole number, the score a learner must earn on the SAT mathematics test to be at the 89.97th percentile is approximately 643.

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