Chapter 9.9, Problem 23ES

Research has shown that the proportion $p$ of the population with $\text{IQs}$ (intelligence quotients) between $\alpha \text{and}\beta$ is approximately

$p=\frac{1}{16\sqrt{2\pi }}{\displaystyle {\int }_{\alpha }^{\beta }{e}^{-\frac{1}{2}{\left(\frac{x-100}{16}\right)}^2}}dx$

Use the first three terms of an appropriate Maclaurin series to estimate the proportion of the population that has $\text{IQs}$ between 100 and 110.