non-Standard

Normal Distributions


The normal distribution will be used to calculate very important probabilities (those allowing use to make claims of confidence of an inferential statistic and be able to test a hypothesis.... you know most of science). The first we will see applications  for normal probability distributions such as finding the percentage of adult women whose height is between 5 feet 4 inches and 5 feet 7 inches, or finding the probability that a new battery will last longer than 4 years.

Just like in the example of the clock-spinner we will find probabilities by finding the area underneath the curve. Yet as we have already seen the equation is very complicated. So one thing we do is always switch to the standard normal as we just saw

Find the areas (VIDEO):

1. To the left of any z value:

Look up the z value in the table and use the area given.

illustration area to left

2. To the right of any z value:

Look up the z value on the table and subtract the area from 1, i.e. 

1Area to Left=Area to Right

illustration area to right

3. Between any two z value:

Look up both z values in the table and subtract the corresponding areas, i.e. using the relationship z2z1 (just as in the pic below) we have

Area to left of z1Area to the left of z2=Area between z1 and z2

illustration area between curves