Question

What score must a learner earn on the ACT composite test in order for the score to be at the 87.49th 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. 32
b. 43
c. 27
d. 19

Answer 1

To find the score that corresponds to the 87.49th percentile on the ACT composite test, we can use the mean and standard deviation provided. Here's how we can calculate it:

1. Calculate the z-score corresponding to the desired percentile using the formula:
z = (x - mean) / standard deviation

2. Rearrange the formula to solve for x:
x = z * standard deviation + mean

3. Substitute the values into the formula:
z = invNorm(0.8749) (using a standard normal distribution table or calculator)
mean = 21.0
standard deviation = 5.2

4. Calculate the score:
x = z * standard deviation + mean

Using these steps, we can calculate the score:

z = invNorm(0.8749) ≈ 1.175

x = 1.175 * 5.2 + 21.0 ≈ 27.39

Rounding up to the nearest whole number, the score that a learner must earn on the ACT composite test to be at the 87.49th percentile is 28.

Therefore, the closest answer is C. 27.

Answer 2

27

Explanation:

You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.

Z-score

The Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.

Score

The corresponding score is ...

X = μ +σZ

X = 21.0 +5.2·1.15 ≈ 27

A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.

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