Question: A school district runs a gifted language program in fifth grade with a selection criterion of 97 th percentile. That is, students who score at

A school district runs a gifted language program in fifth grade with a selection criterion of 97^th percentile. That is, students who score at 97^th percentile or above on a standardized language test are eligible for the gifted program. Answer the following question based on this scenario.

a. What is the probability of randomly drawing a student from the whole population of fifth-graders that would meet the selection criterion for the gifted program? Explain how you determined the answer.

b. If the district has 500 fifth-graders in total, how many will be eligible for the gifted program?

c. If we use a Z distribution to represent all the test scores from the fifth-graders, what is the Z score that serves as the critical (or cutoff) value for this "significant" portion of students who will be eligible for the gifted program?

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