Download THE NORMAL DISTRIBUTION AND THE TI

THE NORMAL DISTRIBUTION AND THE TI-83/84
***Note that normalpdf graphs normal curves, normalcdf finds probabilities.
TO GRAPH A NORMAL CURVE
Press
to access the equation editor. The editor should be completely clear like
this:
Otherwise, clear any equations and turn off all stat plots.
From this window with the cursor after “Y1=”, press
. This selects
“normalpdf“ and pastes it into the equation editor. After the open paren, press
to
enter the variable x, then the values of the mean and the standard deviation separated
by commas. Press
. For example, if the mean is 0 and standard deviation 1, the
screen looks like:
pressing
To set the window, you might have some luck
and going down to “ZoomFit” but I didn’t Press
and set it like
this:
You will need to adjust Xmin, Xmax and Ymax a little for
different values of mean and standard deviation. Remember that by the Emperical Rule,
you’ll see most of your normal curve between +/- 3 standard deviations.
TO FIND A NORMAL PROBABILITY
Press
to bring normalcdf to your home screen like this:
After the open paren, enter the lower (or left-hand) bound of the
area you’re seeking, the upper (or right-hand) bound, the mean and the standard
deviation separated by commas. Press
. Example: If we want the probability
that a normally distributed variable with mean 7.2 and standard deviation 1.3 is between
6 and 9:
The probability is 0.7389.
If the random variable is Z, (standard normal) you can just enter the lower bound and
upper bound and close the parentheses. No mean/standard deviation are needed.
TO GRAPH A NORMAL PROBABILITY
Press
to select “ShadeNorm” and bring it to your home screen
like this:
After the open paren, enter the lower bound, upper bound,
mean and standard deviation separated by commas and close the paren. Example: If
we want to graph the probability that a normally distributed variable with mean 7.2 and
standard deviation 1.3 is between 6 and 9:
viewing window by pressing
-0.1, ymax = about 0.5 like this:
“window” and
You also need to set the
and set xmin = µ - 4, xmax = µ + 4, ymin = about
Then
to escape
to graph. You now have a normal distribution graph and the
probability you were seeking is shaded with the value displayed.
TO FIND AN “X” OR VALUE IN THE DISTRIBUTION
Press
to bring invNorm to your screen like this:
After the open paren, enter the total probability left of the cutoff point you’re seeking, the
mean and the standard deviation separated by commas, then close the parens. For
example, say a normal random variable (x) has a mean of 55 and a standard deviation
of 6. To find the value of the 90th percentile (which is an x) you want this:
And the value of the 90th percentile of a normal distribution with a
mean of 55 and standard deviation 6 is 62.7.