Normal Distributions (Bell Curve): Definition, Word Problems ...

This is the “bell-shaped” curve of the Standard Normal Distribution.

It is a Normal Distribution with mean 0 and standard deviation 1.

It shows you the percent of population:

between 0 and Z (option “0 to Z”)

less than Z (option “Up to Z”)

greater than Z (option “Z onwards”)

It only display values to 0.01%

The Table 

You can likewise utilize the table beneath. The table shows the territory from 0 to Z. 

Rather than one LONG table, we have put the “0.1”s running down, at that point the “0.01”s running along. (Case of how to utilize is beneath)

The standard normal distribution table [18]. | Download Table

Example: Percent of Population Between 0 and 0.45

standard normal distribution 0.45 = 0.1736

Start at the row for 0.4, and read along until 0.45: there is the value 0.1736

And 0.1736 is 17.36%

So 17.36% of the population are between 0 and 0.45 Standard Deviations from the Mean.

Since the bend is balanced, a similar table can be utilized for values going either bearing, so a negative 0.45 additionally has a territory of 0.1736

Example: Percent of Population Z Between -1 and 2

standard normal distribution -1 to +2

From −1 to 0 is the same as from 0 to +1:

At the row for 1.0, first column 1.00, there is the value 0.3413

From 0 to +2 is:

At the row for 2.0, first column 2.00, there is the value 0.4772

Add the two to get the total between -1 and 2:

0.3413 + 0.4772 = 0.8185

And 0.8185 is 81.85%

So 81.85% of the population are between -1 and +2 Standard Deviations from the Mean.