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.
https://davidmlane.com/hyperstat/z_table.html
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.
here's the display.
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