A normal distribution has a mean of and a standard deviation of . What percent of values are from to ​?

Question

A normal distribution has a mean of 4 and a standard deviation of 1. What percent of values are from 4 to 7​?

Answer 1

mean =4

sd = 1

area under the curve between 4 and 7 is found using a z calculator or z tables

7-4 = 3 = z score

4-4=0 = the left z score

area = .49865 = 49.865%

You could have used the empirical rule, but it's slightly less accurate.

by the empirical rule 99.7 fall within 3 standard deviations, leaving .3 outside, and .3/2 = .15 to the right of z score =3. between z=0 and z=3 is 99.7/2 = 49.85. It's off by 0.015