In the United States IQ is normally distributed 1000 190 po

In the United States, IQ is normally distributed (100.0 +/- 19.0 points). IQ values between 130

Solution

for normal distribution

P(X=x) = x-mean/standard deviation/sqrt(n)

given:

from the confidence interval (100 +/- 19)

mean = 100

standard error of mean S = 19

=> Z-score * std/sqrt(n) =19

=> std/sqrt(n) = 19/z-score = 19/1.645 ( assuming 90% confidence interval)

so

P(130 < X < 144) = P(X<144) - P(X < 130)

= P(Z < (144 - 100)/19/1.645) - P( Z < (130 - 100)/19/1.645)

= P(Z<3.809474) - P( Z < 2.59737)

= 0.9999 - 0.9953

= 0.0046 = 0.46%

0.46% population expected to be gifted