Answer to Question #333439 in Statistics and Probability for mimi

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.