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 ( a ≤ x ≤ b ) = 1 0.95 2 π ∫ a b e − ( x − 12.9 ) 2 / 1.805 d x .

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)