Concept of Standard Normal Probabilities

Normal Probabilities:

Comprehension of this table is very important to success!

There is a table that should be utilized to look up standard normal probabilities. The z-score is divided into two parts, the whole number and tenth are looked up all along the left side and the hundredth is looked up across top. The value in intersection of the column and row is the area beneath the curve between zero and z-score looked up.

Since of symmetry of the normal distribution, look up the absolute value of z-score.

Computing Normal Probabilities:

There are many different situations which can occur whenever asked to find out normal probabilities.

Situation                                           Instructions

1) Between zero and                        Look up the area in the table
any number.

2) Between two positives or             Look up both areas in the table and subtract the smaller
Between two negatives.                   from the bigger.

3) Between negative and                  Look up both regions in the table and add up them together.

4) Less than a negative or                Look up the region in the table and subtract from 0.5000
Greater than a positive   

5) Greater than a negative or            Look up the region in the table and add to 0.5000
Less than a positive            

This can be shortened in two rules.

A) When there is just one z-score given, utilize 0.5000 for the second area, or else look up both the z-scores in table.

B) When the two numbers are of similar sign, then subtract; if they are of different signs, then add. When there is just one z-score, then utilize the inequality to find out the second sign (< is negative and > is positive).

Finding z-scores from probabilities:

This is much difficult and needs you to utilize the table inversely. You should look up the area among zero and the value on inner part of the table, and then read the z-score from outside. Lastly, decide if the z-score must be positive or negative, based on whether it was on left side or right side of the mean. Keep in mind that z-scores can be negative, however areas or probabilities can’t be.

Situation                                                 Instructions
1) Area between 0 to a value                 Look up the region in the table
                                                               Make negative if on left side

2) Area in one tail                                   Subtract the region from 0.5000
                                                               Look up the difference in table
                                                               Make negative when in the left tail

3) Area comprising one complete           Subtract 0.5000 from the region
Half (Less than a positive or                   Look up the difference in the table
bigger than negative)                             Make negative if on the left side
    
4) In z units of the mean                        Divide the region by 2
                                                               Look up the quotient in table
                                                               Utilize both the negative and positive z-scores

5) Two tails with equivalent area           Subtract the region from 1.000
(More than z units from the mean)         Divide the area by 2
                                                               Look up the quotient in table
                                                               Utilize both the negative and positive z-scores

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