SOLUTION: Assume that adults have IQ scores that are normally distributed with mean μ=120 and standard deviation of σ=20 . Let x represent the IQ of a randomly selected adult. Solve the
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Question 1183816: Assume that adults have IQ scores that are normally distributed with mean μ=120 and standard deviation of σ=20 . Let x represent the IQ of a randomly selected adult. Solve the following problem. Hint: x=μ+(z⋅σ); z=x−μσ .
Find the IQ score separating the top 86% from the others. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the formula to use is:
z = (x - m) / s
z is the x-score
x is the raw score
m is the raw mean
s is the standard deviation.
you are told that the mean is 120 and the standard deviation is 20.
the formula becomes z = (x - 120) / 20
you want to find the iq separating the top 86% from the others.
this means you want to find the z-score that has an area of .86 to the right of that z-score.
if the area to the right of the z-score is .86, then the area to the left of that z-score is 1 - .6 = .14.
using the following z-score calculator, i find that the z-score with an area of .86 to the right of it is equal to -1.08.
using the same z-score calculator, i find that the z-score with an are of.14 to the left of it is the same z-score of -1.08.
here are the displays.
you can solve for the raw score in the following manner.
start with -1.08 = (x - 120) / 20
multiply both sides by 20 to get:
-1.08 * 20 = x - 120
add 120 to both sides to get:
-1.08 * 20 + 120 = x
solve for x to get:
x = 98.4
the same calculator can solve this for you directly when you place 120 as the mean, rather than 0, and you place 20 as the standard deviation, rather than 1.
