Textbook Problem

Probability The average lengths (from beak to tail) of different species of warblers in the eastern United States are approximately normally distributed with a mean of 12.9 centimeters and a standard deviation of 0.95 centimeter (see figure). The probability that a randomly selected warbler has a length between a and b centimeters is

$P\left(a\le x\le b\right)=\frac{1}{0.95\sqrt{2\pi }}{\displaystyle {\int }_a^b{e}^{-\left(x-12.9\right)2/1.805}}dx.$

Use a graphing utility to approximate the probability that a randomly selected warbler has a length of (a) 13 centimeters or greater and (b) 15 centimeters or greater. (Source: Peterson ’s Field Guide: Eastern Birds)