Question

According to a National Health Survey, American men’s heights are normally distributed with a mean given by 𝜇 = 69.7 inches and a standard deviation given by 𝜎 = 2.8 inches.

a). If a man is randomly selected, find the probability that his height is more 72 inches.

b). If a man is randomly selected, find the probability that his height is between 68 and 72 inches.

Answer 1

a)

$$P(X>72)=1-P(Z\le\dfrac{72-69.7}{2.8})\approx0.2057$$

b)

$$P(68<X<72)=P(Z<\dfrac{72-69.7}{2.8})$$

$$-P(Z\le\dfrac{68-69.7}{2.8})\approx0.5224$$