Math question help please

Question

The heights of adult males in the United States are approximately normally distributed. The mean height is 70 inches (5 feet 10 inches) and the standard deviation is 3 inches. Estimate the probability that a randomly-selected male is between 64 and 71.5 inches tall. Express your answer as a decimal.

Answer 1

z=-2 and z= .5

use z tables or a z calculator

from 65 to 70 is about 95% by the empirical rule; 95/2 = 47.5

from 70 to 71.5 is half a standard deviation

but can't be estimated with just the empirical rule, although it is somewhere between 0 and 34%

maybe 17%

but with tables or a calculator, it's 19.146%

add that to 47.5% to get

66.645%

about 67%

but the 47.5 while reliable is off a little

use the tables or calculator for more accurate estimate