Textbook Problem

Normal Probability The mean height of American men between 20 and 29 years old is 70 inches, and the standard deviation is 2.85 inches. A 20-to 29-year-old man is chosen at random from the population. The probability that he is 6 feet tall or taller is

$P(72\le x<\infty )={\displaystyle \int \begin{array}{c}\infty \\ 72\end{array}\frac{1}{2.85\sqrt{2\pi }}{e}^{-{(x-70)}^2/6.245}dx}$

(Source: National Center for Health Statistics)

1. Use a graphing utility to graph the integrand. Use the graphing utility to convince yourself that the area between the x-axis and the integrand is 1.

2. Use a graphing utility to approximate P(72 ≤ x ∞).

3. Approximate 0.5– P(70 ≤ x ≤ 72) using a graphing utility. Use the graph in part (a) to explain why this result is the same as the answer in part (b).