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 round buttons at the top do not count as a row. Row 1 starts with .

Computing probabilities
The problem is finding P(X <b) where X is a random variance with a specified mean and standard deviation. 
  1. Normalize the X variable by subtracting the mean, then dividing by the standard deviation: Enter X, press The Minus Key: Row 7, Column 4, enter the mean and press The Equals Key: Row 8, Column 5. Press The Divided By Key: Row 6, Column 5, enter the standard deviation and press The Equals Key: Row 8, Column 5.
  2. Press The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (you should see DISTR in blue brackets above the key). You'll see three choices on the screen, press The One Key: Row 7, Column 1 ( P( ).
The problem is finding P(0< X <b) where X is a random variance with a specified mean and standard deviation. 
  1. Normalize the X variable by subtracting the mean, then dividing by the standard deviation: Enter X, press The Minus Key: Row 7, Column 4, enter the mean and press The Equals Key: Row 8, Column 5. Press The Divided By Key: Row 6, Column 5, enter the standard deviation and press The Equals Key: Row 8, Column 5.
  2. Press The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (you should see DISTR in blue brackets above the key). You'll see three choices on the screen, press The Two Key: Row 7, Column 2 ( Q( ).
The problem is finding P( X > b) where X is a random variance with a specified mean and standard deviation. 
  1. Normalize the X variable by subtracting the mean, then dividing by the standard deviation: Enter X, press The Minus Key: Row 7, Column 4, enter the mean and press The Equals Key: Row 8, Column 5. Press The Divided By Key: Row 6, Column 5, enter the standard deviation and press The Equals Key: Row 8, Column 5.
  2. Press The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (you should see DISTR in blue brackets above the key). You'll see three choices on the screen, press The Three Key: Row 7, Column 3 ( R( ).

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=4. Compute P(X < 51).
Solution: The One Key: Row 7, Column 1 The Equals Key: Row 8, Column 5 The Divided By Key: Row 6, Column 5 The Equals Key: Row 8, Column 5 The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (DISTR) The One Key: Row 7, Column 1 ( P( ) The Equals Key: Row 8, Column 5. You should get 0.59871 as the first five decimal places.
Question 2: Let X be a random variable with m=10 and s=8. Compute P(X >12).
Solution:  The One Key: Row 7, Column 1 The Two Key: Row 7, Column 2 The One Key: Row 7, Column 1 The Equals Key: Row 8, Column 5 The Divided By Key: Row 6, Column 5 The Equals Key: Row 8, Column 5 The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (DISTR) The Three Key: Row 7, Column 3 (R( ) The Equals Key: Row 8, Column 5. You should get 0.40129 as the first five decimal places.
Question 3: Let X be a random variable with m=100 and s=12.
P(100 < X < 103).
Solution:  The One Key: Row 7, Column 1 The Three Key: Row 7, Column 3 The One Key: Row 7, Column 1 The Equals Key: Row 8, Column 5 The Divided By Key: Row 6, Column 5 The One Key: Row 7, Column 1 The Two Key: Row 7, Column 2 The Equals Key: Row 8, Column 5 The Shift Key: Round key on the top row, far left. The Three Key: Row 7, Column 3 (DISTR) The Two Key: Row 7, Column 2 ( Q( ) The Equals Key: Row 8, Column 5. You should get 0.09871 as the first five decimal places.
Notice that P will always be 50 more than Q. Also notice that P and R will add up to one.

 

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sample problem set Basic Statistics