Question

The mean and standard deviation of a normal distribution are 150 and 12

respectively. What percentage of values lie between:
a) 138 and 162
b) 126 and 174
c) 126 and 162
d) 162 and 174​

Answer 1

a) (150 - 138) / 12 = 1 deviation or 34%

(162 - 150) / 12 = 1 deviation or 34%

34% + 34% = 68%

b) (150 - 126) / 12 = 2 deviations or 47.5%

(174 - 150) / 12 = 2 deviations or 47.5%

47.5% + 47.5% =95%

c) (150 - 126) / 12 = 2 deviations or 47.5%

(162 - 150) / 12 = 1 deviation or 34%

47.5% + 34% = 81.5%

d) (162 - 150) / 12 = 1 deviation or 34%

(174 - 150) / 12 = 2 deviations or 47.5%

This problem is a little different. We have to subtract 34% from 47.5%

47.5% - 34% = 13.5%