Normal Probabilities

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Entering data
Press . (The 1 gets you into STAT mode; the 0 gets you one-variable statistics.) Enter each number in the list, followed by . 

 

Probabilities on the Normal Distribution
The Problem: Using the mean m and standard deviation s from the data you entered, what is the probability that X is between a and b?   P(a<X<b)
The Solution: There are three variations of this problem and each has a slightly different solution. These commands will not work unless you have entered the data as described above. 
  1. P(X<b): This is called P(t). To invoke it, press The Math Key: Row 1, Column 6 The One Key: Row 6, Column 1, enter b, press The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1 .
  2. P(0<x<b): This is called Q(t), To invoke it, press The Math Key: Row 1, Column 6 The Two Key: Row 6, Column 2, enter b, press The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1 . To solve P( a< x < b), add or subtract Q(t) as necessary.
  3. P(X>a): This is called R(t). To invoke it, press The Math Key: Row 1, Column 6 The Three Key: Row 6, Column 3, enter a, press The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1 .

If the question involves a normalized variable (t instead of x), then the MATH 0 part is left out. (The MATH 0 command normalizes the number.)
Examples: Assume your data follows a normal distribution and has a mean of 100 and a standard deviation of 8.
  1. What is the probability that X is less than 105?
  2. What is the probability that X is larger than 120?
  3. What is the probability that X is between 90 and 110?
  4. What is the probability that X is between 105 and 115?
  5. What is the probability that T is less than 1.5?

Solutions:

  1. The Math Key: Row 1, Column 6 The One Key: Row 6, Column 1 ( P( ) The One Key: Row 6, Column 1 The Zero Key: Row 7, Column 1 The Five Key: Row 5, Column 2 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1
  2. The Math Key: Row 1, Column 6 The Three Key: Row 6, Column 3 ( R( ) The One Key: Row 6, Column 1 The Two Key: Row 6, Column 2 The Zero Key: Row 7, Column 1 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1
  3. We have to add Q(90) and Q(110),  since 90 and 110 are on opposite sides of the mean. The Math Key: Row 1, Column 6 The Two Key: Row 6, Column 2 ( Q( ) The Nine Key: Row 4, Column 3 The Zero Key: Row 7, Column 1 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1 The Plus Key: Row 6, Column 4 The Math Key: Row 1, Column 6 The Two Key: Row 6, Column 2 ( Q( ) The One Key: Row 6, Column 1 The One Key: Row 6, Column 1 The Zero Key: Row 7, Column 1 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1
  4. We have to subtract Q(105) and Q(115), since 105 and 115 are on the same side of the mean. The Math Key: Row 1, Column 6 The Two Key: Row 6, Column 2 ( Q( ) The One Key: Row 6, Column 1 The One Key: Row 6, Column 1 The Five Key: Row 5, Column 2 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1 The Minus Key: Row 6, Column 5 The Math Key: Row 1, Column 6 The Two Key: Row 6, Column 2 ( Q( ) The One Key: Row 6, Column 1 The One Key: Row 6, Column 1 The Zero Key: Row 7, Column 1 The Math Key: Row 1, Column 6 The Zero Key: Row 7, Column 1
  5. The Math Key: Row 1, Column 6 The One Key: Row 6, Column 1 ( P( ) The One Key: Row 6, Column 1 The Decimal Point Key: Row 7, Column 2 The Five Key: Row 5, Column 2
 

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Sharp EL-506W Basic Statistics home page
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