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%