probability and Statistics

Question

Suppose the height in inches of an adult male is normally distributed with μ = 70 inches and σ = 4 inches. What percentage of males have heights within one standard deviation of the mean?

Answer 1

by the empirical rule, 68% are withiin one standard deviation from the mean

68-95-99.7 with 68 within 1, 95 within 2 and 99.7% within 3 standard deviations from the mean

That's a close approximation, true regardless of the mean or standard deviation values

for a closer approximation use z tables or a z calculator

z=-1 to z=1 has area = 0.68269 = 68.269% of the males are within 66 to 74 inches tall