Answer to Question #26126 in Statistics and Probability for Ashton Guthrie

Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score separating the top 10% from the others.

Answer 1

We have normal distribution with mean 100 and standard deviation & 15:
m = 100
sigma = 15
And we know:
P ( x > mean + z*sigma ) = 0.1
or& percentage of values expected to lie in and outside the symmetric interval& mean +- z*sigma = 80 %
From the tables: z = 1.281552 ~ 1.28
Finally,
z*sigma = 1.28*15 = 19.2
Therefore, 10% of all adults have IQ score :
100+19.2=119.2 or more
Answer: 119.2