We are given,
mean = = 100
SD = = 15
First, we need to translate the problem into an area or probability. we can say the kth percentile of a set of data divides the lower k% of a data set from the upper (100-k)%. So the 90th percentile divides the lower 90% from the upper 10% - That is it has about 90% below and about 10% above.
Hence we have to find z for area 0.1
Using excel , =NORMSINV(0.1)
So, z = -1.28
Formula for finding IQ score is,
IQ score = = 100 - (-1.28)* 15
IQ score = 119
Therefore, the 90th percentile for IQ scores is about 119.
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