## Sep 9/13

Sep 9/13

Chap 3 part 2

The Normal Curve and applications

Standardizing values: the z-value:

$z=\frac{x-\mu }{\sigma }$ changes the values in a distribution {x} to a distribution {z} with mean 0 and standard deviation 1.

On the TI: enter the data into a list.

Use STAT CALC 1 [1-Var Stats] to compute the mean and standard deviation.

In a second list, use the formula and the computed mean and standard deviation to provide the z-values.

Cumulative proportions: we use the normalcdf(min, max,mean, stddev) function (accessed by 2nd vars 2) on the TI.

Thus example 3.5 is done with normalcdf(820,1600,1026,209)

Your text shows how a table is used for this computation.

One computes the z-score for 820: (820-1026)/209 = -0.99 and then looks up this z-value in the table of z-values.

Example 3.8 can also be done in this way:

normalcdf(720,820,1026,209)= 0.09057 = 9.057%

Note that the calculator does not have to round off the z-values and thus gives a slightly different result.

If we compute normalcdf(-1.46, -.99) we get the text result.

In order to find the z- or x-values which correspond to a certain percentage of area under the normal curve, we use the function InvNorm. This is (alas) a left-tail function, giving the z- or x- value for the left tail. So to find the top 10%, we look for the 90% value:

InvNorm(.9, 504, 111) = 646.25.

Finding quartiles can also be done using InvNorm, always remembering that we are using the left tail.

See example 3.11: InvNorm(.25, 170,30) = 149.76.

Please review the summary on pages 86 ff in the text.