Question

IQ scores for adults are normally distributed with mean of 100 and standard deviation of 15. What percent of adults have IQ scores greater than 130?

Answer 1

Denote by $X$ a random variable that corresponds to IQ scores. $X$ is normally distributed with mean of $100$ and standard deviation of $15$. The aim is to find $P(X\geq130)$. The probability density function of $X$ is: $f(x)=\frac{1}{15\sqrt{2\pi}}e^{-\frac12\left(\frac{x-100}{15}\right)^2}$. Thus, $P(X\geq130)=\frac{1}{15\sqrt{2\pi}}\int_{130}^{+\infty}e^{-\frac12\left(\frac{x-100}{15}\right)^2}dx\approx0.02275$

Answer: $2.275$% of adults have IQ scores greater than $130$. The answer is rounded to $3$ decimal places.