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Inverse Normal Distribution SAT and ACT Scores

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For a given population of high school seniors, the schoolastic aptitude test (SAT) in mathemathics has a mean score of 500 with the standard deviation of 100. Another widely used test is the American college testing (ACT)exam. The mathemathics portion of the ACT mean of 18 and a standard deviation of 6.

(a) Suppose that an engeneering school honors program will accept only high school seniors with a mathemathics SAT or ACT score in the top 10%. What is the minimum SAT score in mathemathics for this program? What is the minimum for ACT score for this program?

(b) Suppose that an engeneering school will accept only high school seniors with a mathemathics SAT or ACT score in the top 20%. What is the minimum SAT score in mathemathics for this program? What is the minimum ACT score in mathemathics for this program?

(c) Suppose that an engeneering school will accept only high school seniors with a mathemathics SAT or ACT score in the top 60%. What is the minimum SAT score in mathemathics for this program? What is the minimum ACT score in mathemathics for this program?

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Solution Summary

All three problems solved to find out the cut-off scores.

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SAT: M = 500, s = 100, Minimum score x = M + z(s) and ACT: M = 18, s = 6, Minimum score x = M + z(s)

(a) Area under the standard normal curve ...

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