Question

The interval is in the middle of the normal distribution and is symmetrical about x=0. Compare results from the empirical rule statements to the values you get when using the normal table.  What did you find?

Answer 1

The values that we get from the empirical rule statement and the normal distribution table are quite similar , they are basically taken from the table and given to make the calculations easier for some examples.

Example : empirical rule states that the area under normal curve within the one standard deviation is 68%.

Now looking into table we find that the exact value is = 68.26 % which is quite similar to above empirical rule value.

In case we want highly accurate answers than it is recommended to use the normal distribution table rather than empirical rules.