The Normal Distribution on the TI-83/84
The TI-83/84 can perform several statistical functions relative to normal
distributions.
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A. Press the [2 ] and [VARS] keys to get to the DISTR menu. Here are several
of the statistical functions of the calculator. The screen pictured on the left is the
TI 83 or the TI 84 which does not have the latest operating system. The screen on
the right it the TI 84 with the latest operating system.
TI 84 with latest
OS
1. The first choice, normalpdf gives you’re the normal probability density function
for a given mean and standard deviation. We will look at this later.
2. The second choice is the normal cumulative density function. This is the one
we will use to calculate probabilities.
If you press “enter”, you will see
The program is waiting for some
parameters. It is waiting for the
LUMS. That is Lower limit of the random variable, Upper limit of the random
variable, Mean of the distribution, Standard deviation of the distribution.
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For example, if you want the p  35  x  70 for a normal random variable X with a
mean of 75 and standard deviation of 10, then we would enter
Note; if the mean and stan. dev. are left out, they
are assumed to be 0 and 1.
We press “enter” to get a probability
of .309
3. The first choice, normalpdf can be used to give you a picture of the normal
probability distribution graph. Recall the formula
this is the normal probability density function.
If you open the graph menu (the equation editor
normalpdf in the graph menu,
) and then open the
the screen above will give you a graph of a normal function with a mean of 75 and
a standard deviation of 10. (If you leave out the mean and standard deviation, the
calculator assumes they are 0 and 1 respectively)
To see the graph, set the window like this screen
And then press “graph”. You should get a picture
like this;
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4. The third choice, invNorm, finds the z-score or raw score with a given area to
the left.
The format for this command is: invNorm(area, mean, stand. dev.)
If the mean and stand. dev. are left out they are assumed to be 0 and 1.
Note, the x value that is calculated is associated with an area to the left of the x
value.
In the screen below, the calculator will return the z score with an area of .8413447
to the left. This turns out to be approximately 1.
The rest if the choices under this menu we will get to later.
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B. Press the [2 ] and [VARS] keys to get to the DISTR menu again.
If you move the cursor over to the DRAW menu, you should see the following:
The format for the ShadeNorm command is:
ShadeNorm(lowerbound, upperbound, mean, stand. dev.)
If we enter ShadeNorm (70,80,75,5)
The area between 70 and 80 for a normal
distribution with a mean of 75 and a sd of 5 is
drawn and is equal to about .683. The area is
given at the bottom of the screen.
Note; this area is the area within one
standard deviation of the mean, which does
contain about 68% of the area under the curve.
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