SOLUTION: Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 20. Find P(sub/small)14, which is the IQ score separating the bottom

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Question 445434: Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 20. Find P(sub/small)14, which is the IQ score separating the bottom 14% from the top 86%.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

IQ scores that are normally distributed with a mu of 105 and a sigmaof 20

Find P%5B14%5D

  *Note: z+=+%28x+-+mu%29%2F%28sigma%29

 lower 14% then z = -1.0803  NORMSINV(0.14)          

 -1.0803 = (x - 105)/20

 105 - 20*1.0803 = 83.394

 top 86% then z = 1.0803     NORMSINV(0.86)

   105 + .20*1.0803 = 126.606



     126.6 - 83.4 = 43 IQ points separating the bottom 14% from the top 86%.