Statistics Examples Normal Distributions
Find the Probability Using the Mean and Standard Deviation
, ,
Step 1
The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.
Step 2
Step 2.1
Fill in the known values.
Step 2.2
Simplify the expression.
Step 2.2.1
Simplify the numerator.
Step 2.2.1.1
Multiply by .
Step 2.2.1.2
Subtract from .
Step 2.2.2
Divide by .
Step 3
The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.
Step 4
Step 4.1
Fill in the known values.
Step 4.2
Simplify the expression.
Step 4.2.1
Simplify the numerator.
Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Subtract from .
Step 4.2.2
Divide by .
Step 5
Find the value in a look up table of the probability of a z-score of less than .
has an area under the curve
Step 6
Find the value in a look up table of the probability of a z-score of less than .
has an area under the curve
Step 7
To find the area between the two z-scores, subtract the smaller z-score value from the larger one. For any negative z-score, change the sign of the result to negative.
Step 8
Step 8.1
Multiply by .
Step 8.2
Add and .