Question

Given a mean of 150 and a standard deviation of 25 Define the interval about the mean that contains 95% of the data.

Answer 1

By normal curve symmetry 

from normal table 
we have z = 1.15 , z = -1.15 

z = (x - mean) / sigma 
1.15 = (x - 150) / 25 
x = 178.75 


z = (x - mean) / sigma 
-1.15 = (x - 150) / 25 
x = 121.25 

interval is (121.25 , 178.75) 

Pr((121.25-150)/25 < x < (178.75-150)/25) 
is about 75%