Problems with normal probabilities

The position of the graphically represented keys can be found by moving your mouse on top of the graphic. 
The row of function keys: f1, f2, etc. do not count as a row. Row 1 starts with the blue 2nd key.

Drawing a normal curve
The problem is finding P(a < X < b) where X is a random variance with a specified mean and standard deviation. Also, drawing the graph.
Get to the Stats/List Editor. That is:
Press The Apps Key: Row 2, Column 3, then arrow over to the Stats/List Editor. (Which arrows you push depends on which APP you last used.) Press The Enter Key: Row 9, Column 5 The Enter Key: Row 9, Column 5. 
  1. Press The F 5 Key: Top Row rightmost key and the Distr menu will fall. 
  2. Choose The One Key: Row 8, Column 2 for 1:Shade.... Then choose The One Key: Row 8, Column 2 for 1:Shade Normal....
  3. Enter a, the lower endpoint, and press The Down Arrow Key: Upper Right.
  4. Enter b, the upper endpoint, and press The Down Arrow Key: Upper Right.
  5. Enter the mean, m, and press The Down Arrow Key: Upper Right .
  6. Enter the standard deviation, s, and press The Down Arrow Key: Upper Right.
  7. Press The Enter Key: Row 9, Column 5 to see the graph. At the bottom of the graph, the area under the curve, that is the probability of being in that interval, will appear.
Note: If you want to graph P(X < b), choose a to be very small, that is, more than three standard deviations below the mean. Example if m is 4 and s is 2, then a should be -4 or less.

If you want to graph P(X > a), choose b to be very big, that is, more than three standard deviations above the mean. Example if m is 4 and s is 2, then b should be 10 or more.

 

Computing probabilities without the graph
The problem is finding P(a < X <b) where X is a random variance with a specified mean and standard deviation. 
Press The Apps Key: Row ???, Column ????, then arrow over to the Stats/List Editor. (Which arrows you push depends on which APP you last used.) Press The Enter Key: Row 9, Column 5 The Enter Key: Row 9, Column 5. 
  1. Press The F 5 Key: Top Row rightmost key and the Distr menu will fall. Choose The Four Key: Row 7, Column 2 for 4: Normal Cdf.... A new window will appear. 
  2. Enter a, the lower endpoint, and press The Down Arrow Key: Upper Right.
  3. Enter b, the upper endpoint, and press The Down Arrow Key: Upper Right.
  4. Enter the mean, m, and press The Down Arrow Key: Upper Right.
  5. Enter the standard deviation, s, and press The Down Arrow Key: Upper Right.
  6. Press The Enter Key: Row 9, Column 5 and a new window will appear. The first line tells you the cdf, the probability of being in that interval.

Worked Out Examples

In the following examples, we list the exact key sequence used to find the answer.  We will list the keys by the main symbol on the key.  In parentheses, we will list a helpful mnemonic, e.g. we will list ex as (ex).

Question 1: Let X be a random variable with m=50 and s=2. Draw a normal curve to compute and illustrate 
P(49< X <52).
Solution:

 The F 5 Key: Top Row rightmost key (Distr menu) The One Key: Row 8, Column 2 (1:Shade...) The One Key: Row 8, Column 2 (1:Shade Normal...) The Four Key: Row 7, Column 2 The Nine Key: Row 6, Column 4 (low) The Down Arrow Key: Upper Right The Five Key: Row 7, Column 3 The Two Key: Row 8, Column 3 (high) The Down Arrow Key: Upper Right The Five Key: Row 7, Column 3 The Zero Key: Row 9, Column 2 (m) The Down Arrow Key: Upper Right The Two Key: Row 8, Column 3 The Down Arrow Key: Upper Right (s) The Enter Key: Row 9, Column 5.
It should say Area=.532807 at the bottom of the graph.

Graph should look like this:

Normal graph shaded from 49 to 52

Note: Graph window has x-min=45, x-max=55, y-min=-0.1 and y-max=0.3.
Question 2: Let X be a random variable with m=10 and s=3. Compute, but don't draw the graph for P(X >7).
Solution:

 The F 5 Key: Top Row rightmost key ( Distr menu) The Four Key: Row 7, Column 2 (4:Normal Cdf) The Seven Key: Row 6, Column 2 (low) The Down Arrow Key: Upper Right The Three Key: Row 8, Column 4 The Zero Key: Row 9, Column 2 (high, your number here may vary) The Down Arrow Key: Upper Right The One Key: Row 8, Column 2 The Zero Key: Row 9, Column 2 (m) The Down Arrow Key: Upper Right The Three Key: Row 8, Column 4 The Down Arrow Key: Upper Right (s) The Enter Key: Row 9, Column 5.
It should say Cdf = .84134474 at the top of the window.
Question 3: Let X be a random variable with m=100 and s=6. Draw a normal curve to compute and illustrate 
P(X < 90).
Solution:

 The F 5 Key: Top Row rightmost key ( Distr menu) The One Key: Row 8, Column 2 (1:Shade...) The One Key: Row 8, Column 2 ( 1:Shade Normal...) The Zero Key: Row 9, Column 2 (low) The Down Arrow Key: Upper Right The Nine Key: Row 6, Column 4 The Five Key: Row 7, Column 3 (high) The Down Arrow Key: Upper Right The One Key: Row 8, Column 2 The Zero Key: Row 9, Column 2 The Zero Key: Row 9, Column 2 (m) The Down Arrow Key: Upper Right The Six Key: Row 7, Column 4 The Down Arrow Key: Upper Right (s) The Enter Key: Row 9, Column 5.
It should say Area=.202328 at the bottom of the graph.
Graph should look like: 

Note: Graph window has x-min=82, x-max=118, y-min=-0.1 and y-max=0.3.

 

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TI's online manual sample problem set home page
Scatterplots and Histograms Hypothesis Tests and Confidence Intervals Basic Statistics
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