The mean height of American men between 20 and 29 years old is 70 inches, and the

Chapter 8, Problem 111

(choose chapter or problem)

Normal Probability The mean height of American men between 20 and 29 years old is 70 inches, and the standard deviation is 3 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

\(P(72 \leq x<\infty)=\int_{72}^{\infty} \frac{1}{3 \sqrt{2 \pi}} e^{-(x-70)^{2} / 18} d x\).

(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 \(P(72 \leq x<\infty)\).

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

Text Transcription:

P(72 leq x<infty)=int_72^infty 1/3 sqrt 2 pi e^-(x-70)^2 / 18 dx

P(72 leq x<infty)

0.5-P(70 leq x leq 72)