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   ≤   x   <   ∞ )   =   ∫ 72 ∞ 1 2.85   2 π e − ( x   −   70 ) 2 / 6.245 d x

(Source: National Center for Health Statistics)

(a) 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.

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

(c) 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).