Chapter 3

Modeling Distributions of Data

The standard Normal distribution

the Normal distribution with mean 0 and standard deviation 1

z has the standard Normal distribution...

On TI-84 Plus C Silver Edition, the area under the standard Normal curve for a z-value can be found by entering the following:

Example 1:  Joestat hands out cards with z-scores on them.  Your job is to find the probability that your neighbor has a lower ranked card.  You have a z-score of -.92.

Example 2:  What is the probability that your neighbor has a higher ranked card? 

Example 3: Your z-score is -.92 and your neighbors z-score is 1.37. Find the probability that your friend has a card ranked between you and your neighbor.

2nd VARS2. Normalcdf(-99999,-.92)ENTER

2nd VARS2. Normalcdf(-.92,-99999)ENTER

2nd VARS2. Normalcdf(-.92,1.34)ENTER

To calculate a probability given a z-score using your TI-84 calculator we use the normalcdf function.normalcdf(Minimum Outcome, Maximum outcome)

Set your window settings, by pressing [WINDOW] and setting your values to xmin = - 5, xmax = 5, ymin = -.1 and ymax = .5.Press 2nd VARS (DISTR), scroll right to DRAW, 1:ShadeNormEnter -99999 as a lower limit, .1 as the upper limit (leave the mean and std dev as default 0 and 1)Pick a color.Press [DRAW].The probability associated with a Z-score of .1 is shown in the bottom-left corner.

And the reverse...

Find the z-score for a percentage representing part of the area under a curve.

2nd VARSInvNorm(.7038)ENTER

Returns the z-score representing 70.38% of the area under the curve