A highly selective boarding school will only admit students who place at least 1.5 z-scores above the mean on a standardized test that has a mean of 110 and a standard deviation of 12. What is the minimum score that an applicant must make on the test to be accepted?

Question

Mathematics

Zion Combs

17 July, 20:24

A highly selective boarding school will only admit students who place at least 1.5 z-scores above the mean on a standardized test that has a mean of 110 and a standard deviation of 12. What is the minimum score that an applicant must make on the test to be accepted?

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Answers (1)

Know the Answer?

Esteban Wade · Answer 1

An applicant must score a minimum of 128

Step-by-step explanation:

To solve this question, we make use of the z-score formula.

Z = (X - mean) / standard deviation

Firstly, let's list out the parameters from the question. From the question, we can deduce that:

Z = 1.5

X = ?

Mean = 110

Standard deviation = 12

1.5 = (X-110) / 12

18 = X - 110

X = 110 + 18

X = 128