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Fundamentals of Statistics Section 95 TI-83 Instructions - Z scores from Probabilities Instructor: Pete WildmanFall Semester 1999 |
Using the TI-83 instead of the normal table to calculate z-scores corresponding to probabilities
The process of finding a particular score for given probability is difficult and somewhat inaccurate with the normal table. But with the TI-83 calculator you can do this quickly, accurately and painlessly
STANDARD NORMAL PROBABILITY PROBLEMS
To see how consider this example
You manufacture thermometers and these thermometers should measure 
at the freezing point of water. You test a large sample of these thermometers and discover that the distribution of actual temperatures measured at the freezing point of water follows a normal distribution with a mean of 0 degrees and a standard deviation of 1 degree.
Let's find 
, the score corresponding to the 80th percentile. Since the area under the normal curve is 1 and since the probability and z-score are directly related, we are looking for the score where the cumulative density function has a value of .8. If we use the invNorm function we can do this easily!
Hit 2nd then the VARS key to get the distribution menu - your screen should look like this:
Now hit 3 for invNorm - You should see this on your screen
Now enter the desired percentile in this case .8 and hit enter you should see the following screen. How does this answer compare with the table answer:
How about another problem
- Let's find
- the 10th percentile
Again, hit 2nd ,VARS, 3 for invNorm and enter .1 for the desired probability and hit enter. Did you get the following? How does this compare with the table method?
NONSTANDARD PROBABILITY PROBLEMS
Recall to do these problems with the table you needed to find a z-score and then use the standard normal table. The TI-83 can do these problems directly without calculating the z-score and it gives you a more accurate answer than the table gives you - here is how
Remember this problem
The highway miles per gallon of sporty and compact cars were determined to be normally distributed with a mean of 33.78 and a standard deviation of 9.94. What MPG rating corresponds to the 95th percentile?
You could still calculate the z-score and use the standard normal distribution - but you don't need to do so!
Hit 2nd, VARS, 3 for invNorm, enter 95, a comma, enter the mean (33.78) and the standard deviation (9.94) Your screen should look as follows:
Hit enter to get your answer - how does the screen below compare to the table method?
SUMMARY - TO GET A Z-SCORE CORRESPONDING TO A PROBABILITY