Question 1204469: 3. Suppose that a school district wants to start a program for gifted students. The participants in the program are to be chosen on the basis of IQ scores (normal with = 100, = 15). If the school district wants only the top 2.5% of students to participate in the program, what should be the IQ score that students must exceed to be accepted?
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
Suppose that a school district wants to start a program for gifted students.
The participants in the program are to be chosen on the basis of IQ scores (normal with mean = 100, SD = 15).
If the school district wants only the top 2.5% of students to participate in the program,
what should be the IQ score that students must exceed to be accepted?
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They want you find a score z on the IQ number axis in such a way that the area
under the specialized normal curve to the right of this z-score be 2.5%, or 0.025.
For it, use the standard function invNorm of your regular calculator TI-83/84.
It has this form
area mean SD <<<---=== formatting pattern
z = invNorm(0.975, 100, 15)
0.975 here is 1-0.025, the area on the left of z-score.
The function invNorm gives the answer z = 129.399.
The school district should accept the students whose IQ score is 129.399 or above.
If they want the answer in integer numbers and do not want yield the level of students,
then they should round to greater integer IQ >= 130.
Solved.
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Alternatively, instead of regular calculator TI-83/84, you can use an online
free of charge calculator of this web-page https://davidmlane.com/hyperstat/z_table.html
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