The Normal Distribution on the TI-83
The TI-83 can perform several statistical functions. Press the
[2nd] and [VARS] keys to get to the DISTR menu, here are several of the
statistical functions of the calculator.
1.
The first choice, normalpdf gives you’re the normal probability
density function for a given mean and standard deviation. Recall the
formula
f ( x) =
e
− ( x − µ )2
2σ 2
, this is the normal probability density function.
2πσ
if you are under the graph menu
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)
2. The second choice, normalcdf gives you the normal distribution
probabilities. The format for this command is
normalcdf(lowerbound, upperbound, mean, stand. dev),
if the mean and stan. dev. are left out, they are assumed to be 0 and 1.
So the P(0 < Z < 1) =.34213 for a standard normal curve, and
P(75 < X < 80) = .3412 for a normal distribution with a mean of 75
and a sd of 5
(notice a score of 80 here corresponds to a z-score of 1)
3. The third choice finds the z-score or raw score for a given area.
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. Recall on a standard normal curve there is about 34.13% of the
area between 0 and 1, so for a z-score of 1, the area to the left should be
about
.5 + .3413 = .8413.
The inverse normal gave us a z-score of .9998 which is approximately 1.
The actual area between z-scores of 0 and 1 is .3413447399, so the area to
the left of 1 is .5 + .3413447399 = .8413447399
The rest if the choices under this menu we will get to later. 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.)
So
yields
So a the are between 70 and 80 for a normal distribution with a mean of 75
and a sd of 5 is about .682689, note this area is the area within one
standard deviation of the mean, which does contain about 68% of the area
under the curve.