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, you must 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.
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%)
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.
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We can use the Complement Of An Event Formula to calculate the solution.
1-.1788 = .8212
Your z-scores is -.92 and your neighbors z-score is 1.37.
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.October 18, 2014 by Joseph Schumacher