Math 160H - CooleyTI Calculator Handout #4 OCC

The Normal Distribution on the TI-83+/TI-84+ Calculator

The TI-83 can perform several statistical functions based about the normal distribution.

Part 1: Using the normalpdf Function

  • The normalpdf( function gives you the normal probability density function for a given mean and standard deviation. The formula for the normal probability density function is . With a specific mean μ, and a specific standard deviation σ, the graph for the normal probability density function will be displayed on your calculator.
  • The syntax for the normalpdf( function is (variable, mean, standard deviation).
  • Note: If you leave out the mean and standard deviation, the calculator assumes they are 0 and 1, respectively.

Example: Plot a normal probability plot with mean 75 and standard deviation 10.

1)Press Y = menu. Now, press 2nd and then VARS, which is the DISTR menu.The cursor should already be on

DISTRand 1:normalpdf(. (See Figure 1). So, press ENTER.

2)Now, we must enter the syntax for the normalpdf( function. So, press X,T,θ,n, followed by a comma.

3)Then, enter in the value for the mean, followed by a comma.

4)Lastly, enter in the value for the standard deviation, followed by ) . See Figure 2.

Figure 1 Figure 2

5)Now, Press GRAPH. More than likely, nothing will be displayed. Sometimes the zoomfit function, might take

care of this, however, we are going to resize the window, so the entire graph is displayed on the screen.

6)Set the window under the following constraints:

Xmin:

Xmax:

Xscl: any value

Ymin: 0

Ymax:

Yscl: any value

Xres: 1

Yres: 1

7)Lastly, press GRAPH under the new window settings. The graph of the normal probability density function will then be displayed. Using the trace feature, the result is shown in Figure 3.

Figure 3

Part 2: Plot a Normal pdf with shaded region for P(aXb)

  • The syntax for the plot of a Normal pdf for a shaded region is (a, b, μ,σ) where a is the lower bound and b is the upper bound.
  • Note: If you leave out the mean and standard deviation, the calculator assumes they are 0 and 1, respectively.

Example: Plot a normal probability plot with shaded region for , where μ = 75 and σ = 10.

1)Press 2nd and then VARS, which is the DISTR menu. The cursor should already be on DISTR and

1:normalpdf(. Cursor over to DRAW, and now the cursor is on the DRAW menu and 1:ShadeNorm(

(See Figure 4). So, press ENTER.

2)Now, we must enter the syntax for the ShadeNorm( function. So, enter in the lower bound, a, followed by a

comma. (In our example use 65).

3)Then, enter in the upper bound, b, followed by a comma. (In our example, use 90).

3)Then, enter in the value for the mean, followed by a comma. (In our example, use 75).

4)Lastly, enter in the value for the standard deviation, followed by ) . (In our example, use 10).When your

results are entered, press ENTER.The plot is shown in Figure 5.

Figure 4 Figure 5

Thus, .

Example: Plot a normal probability plot with shaded region for , whereμ = 75 and σ = 10.

Solution:Repeat the steps from above, however, b is technically unbounded, since means.

So, if either a or b is not bounded, then you must enter in an extreme value, since ∞ is not an entry that the

calculator accepts. So, just use for –∞ and for ∞. To enter these numbers, use the following

syntax: - , 1 ,EE , 9 , 9 and 1 ,EE , 9 , 9 respectively. The plot is shown in Figure 6.

Figure 6

Thus, .

Note: If you have already graphed a normal probability plot and are trying to graph a second normal probability

plot on the same window settings, the plot will not reset, instead it will just copy over the previous one and

merge together any shaded sections from both graphs, which will result in an incorrect graph. A quick fix for

this is to adjust the window setting Xscl. Simply make it something different. Since, it will not affect the

outcome of the plot, the calculator will create a new plot, deleting the previous plot.
Part 3: Using the normalcdf Function: Calculating the area under a normal curve ; P(aXb)

  • Here, we can calculate the area under a normal curve, without actually plotting a Normal pdf as in Part 2. Instead, we will use the normalcdf( function, which stands for the normal cumulative density function.
  • The syntax for the normalcdf( function for a shaded region is (a, b, μ,σ) where a is the lower bound and b is the upper bound.
  • Note: If you leave out the mean and standard deviation, the calculator assumes they are 0 and 1, respectively.

Example: Find , if X comes from a normal distribution withμ = 75 and σ = 10.

1)Press 2nd and then VARS, which is the DISTR menu. The cursor should already be on DISTRand

1:normalpdf(. Cursor down to 2:normalcdf( and press ENTER.

2)Now, we must enter the syntax for the normalcdf( function. So, enter in the lower bound, a, followed by a

comma. (In our example use 65).

3)Then, enter in the upper bound, b, followed by a comma. (In our example, use 90).

3)Then, enter in the value for the mean, followed by a comma. (In our example, use 75).

4)Lastly, enter in the value for the standard deviation, followed by ) . (In our example, use 10).When your

results are entered, press ENTER. The result and a screenshot is shown in Figure 7.

Figure 7

Thus, .

Example:Find , if X comes from a normal distribution withμ = 75 and σ = 10.

Solution:Repeat the steps from above, however, b is technically unbounded, since means .

So, if either a or b is not bounded, then you must enter in an extreme value, since ∞ is not an entry that the

calculator accepts. So, just use for –∞ and for ∞. To enter these numbers, use the following

syntax: - , 1 ,EE , 9 , 9 and 1 ,EE , 9 , 9 respectively.The result and screenshot is shown in

Figure 8.

Figure 8

Thus, .