Probability Given a Z-scores | TI-84 or TI-83 Example

The probability is the same as the area under the curve for a normal distribution.  Now Joestat wants to help you find the probabilities of a given z-score using the following examples.

To calculate a probability given a z-score using your TI-84 or TI-83 calculator we use the normalcdf function.
normalcdf(Minimum Outcome, Maximum outcome).

Example 1:  Joestat hands out cards with z-scores on them.  Your job is to find a was you can use your TI-84 or TI-83 calculator to find the probability that your neighbor has a lower ranked card.  You have a z-score of -.92.

Problem 1:  Find the probability that your neighbor has a lower ranked card.
First: Sketch out the the problem.
Normal Probability Distribution image, find the area of the teal shade.

Second: Using the image we can determine we are interested in the teal shade.  We can also may clarify that the area is less than 50%.  So if you get an area above 50% recalculate, it’s more than likely user error.  (Note: Mu to one end is 50%)

Third: We calculate the solution.
[2ND] | [VARS] | [2] | [-] | [9] | [9] | [9] | [9] | [9] | [,] | [-] | [.] | [9] | [2] | [)] | [ENTER]
Normal Probability Distrubiton proportion using ti-83 and ti-84 is .1788

Solution: .1788

Problem 2:  What is the probability that your neighbor has a higher ranked card?  Use your TI-84 or TI-83 calculator to find your neighbors proportion given your z-score.

First Sketch the problem, which is shown above.

Second:  This time we care about the orange area.  From the graph we can determine that the probability should be greater than 50%.
Solving the problem using your TI-84 and TI-83 calculator.
[2ND] | [VARS] | [2] | [-] | [.] | [9] | [2] | [,] | [9] | [9] | [9] | [9] | [9] | [)] | [ENTER]
Solution using the TI-84 or TI-83 normalcdf( function is .8212

Alternate Solution:
We can use the Complement Of An Event Formula to calculate the solution.
1-.1788 = .8212

Example 2:
Your z-scores is -.92 and your neighbors z-score is 1.37.

Problem 1:
Find the probability that your friend Joestat has a card ranked between you and your neighbor.z-score-to-population-sketch
From the sketch we can determine that the orange area is greater than 50%.

[2ND] | [VARS] | [2] | [-] | [.] | [9] |[2] | [,] | [1] | [.] | [3] | [4]
TI-84 going form zscore to percentage is .7311

Problem 2:  Find the probability that Joestat has a lower ranked card than you or a higher ranked card than your friend.
Solution: Use the rule of complements 1-.7311 = .2689

Congratulations you have found a way to handle every situation for finding proportions using a z-score with your TI-84 and TI-83 calculator.

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Last Modified on February 19, 2013 by JoeStat

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