Question

We know that the IQ test has a population mean of 100 and a population standard deviation of 16 (we know this because IQ tests are normed on thousands of people and these are the consistent values). The principals of a consortium of 3 high schools for the gifted want to know if their students are above average. They give the IQ test to all their students and here are the results:

School A = 104 School B = 116 School C = 98 a.)

a) Which school has the best claim that its students are gifted (assuming you accept an IQ score as a valid measure of gifted)?

b.) What about the other two schools? Would you accept their claim that their student bodies are gifted? Why or why not?

Answer 1

Solution : let x is a random Variable and Variable and follows X WN(4,2) follows normal distribution Here [xN X~ N(100, 16²) Meanu = 100 Standard deviation B = 16 formula We have X-4 Z = 2) Where ZAN(o,) formula, the population value in to According Z = 100-100 16 O population Value School A Z = 104 700 16 = 0.25 School B Z (16-100 16 = 1 =-0.12 cs Scanned with CamScanner Scan School 98-100 16 Z =

Ang a The School B Because on its students are 1 Standard overage deviation above the mean. other schools 'average mean (z=0) I Os are much closed to the population Any : I would not accept the claim of Schools A and C, because their average Z Score is so close to o (which is equivalent to saying that their average JOB are very Close to the population average). Although the z for School A is positive ive (+ 0-25) and the z for school B is negative (-0.12) the important factor is that their cu are both close to the mean for all students their everages Scanned with CamScanner