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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Finding Probability

In practice, we rarely use the Empirical Rule to report probabilities. Why? Because we rarely have values that are round distances from the mean. What I mean by that is it's not likely that we have a value that is exactly 2 standard deviations from the mean. It's more realistic to have a value that is 2.81 standard deviations from the mean. However, it's hard to compute an accurate probability estimate for that using the Empirical Rule. This is why we use technology or a Z-Table to estimate probability on the standard normal distribution.

 

Z-Table

There are different formats for this table, so it's recommended that you utilize the table that is provided in your course resources if your course uses the table method. This will reduce confusion when trying to follow the examples in your course and to check your work. If you have questions about how to read the table, ask your instructor or connect with one of our stats coaches.

 

TI-83/84 Graphing Calculator

Here are the basic steps for using this tool to find the probability:

  1. press 2ND then VARS (DISTR)
  2. choose normalcdf - we want "cdf" since we're looking for cumulative probability
  3. depending on your calculator, you may see a window asking for values or you may see "normalcdf(" in the screen. In either case, here's what it's asking for:
    • lower: what is the lower limit of the area you're trying to find? (if your lower limit is the left tail, use negative infinity or -99999)
    • upper: what is the upper limit of the area you're trying to find? (if your upper limit is the right tail, use positive infinity or 99999)
    • µ: what is the mean of the distribution? (if you're working with a z-score, this is the mean of the z-distribution: 0)
    • σ: what is the standard deviation of the distribution? (if you're working with a z-score, this is the st. dev. of the z-distribution: 1)
  4. paste the information onto the next screen using the option there or, if you do not have the list, simply fill in the correct values where they belong: normalcdf(lower,upper,µ,σ)
  5. press Enter to receive the probability for the area you entered

 

Excel

Here are the basic steps for using this tool to find the probability:

  1. click into a new cell and type =NORM.S.DIST(
    • you could also go to Formulas > More Functions > Statistical and choose NORM.S.DIST from the list.
  2. enter the z-score of interest
    • if typing in the cell: =NORM.S.DIST(z,true)
      • replace "z" with your z-score
    • if going through the Formulas, enter the z-score in the first box and "true" in the cumulative box

This will return the probability below the z-score that's entered. This is important to keep in mind incase you're looking for the area above the z-score.

 

For more support with any of these methods, please reach out using ASC Chat for assistance in connecting with a coach that can engage you in guided practice using the method that's required for your course.