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.

Problem 1: Find the probability that your neighbor has a lower ranked card.

First: Sketch out the the problem.

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]

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]

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.

From the sketch we can determine that the orange area is greater than 50%.

[2ND] | [VARS] | [2] | [-] | [.] | [9] |[2] | [,] | [1] | [.] | [3] | [4]

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.

Last Modified on October 18, 2014 by Joseph Schumacher