## StatCrunch – Probability Calculators

*March 18, 2010 at 5:23 am* *
2 comments *

My statistics classes have just finished the unit on probability distributions – binomial, Poisson, and normal. This is the first semester using StatCrunch in this course, so I thought I’d put together a short “how to” article on how to use StatCrunch with these three distributions.

**Binomial Distribution**

The binomial calculator in StatCrunch can be accessed through **Stat > Calculators > Binomial**. The dialog box asks you to enter *n*, *p*, and *x.* You also enter an inequality or equal sign: <, <, >, >, or =. The calculator calculates the probability and displays a probability histogram. Values of *x* in your interval appear in red in the probability histogram.

One slight problem arises when trying to determine P(*a* < *x* < *b*). You must first calculate P(*x* < *b*), and from this result subtract P(*x* < *a*). Alternatively, you could find P(*x* = *a*), P(*x* = *a* + 1), …, P(*x* = *b*) and total these results.

**Poisson Distribution**

The Poisson calculator in StatCrunch can be accessed through **Stat > Calculators > Poisson**. The dialog box asks you to enter the mean and *x**.* You also enter an inequality or equal sign: <, <, >, >, or =. The calculator calculates the probability and displays a probability histogram. Values of *x* in your interval appear in red in the probability histogram.

As with the binomial calculator, you cannot directly calculate P(*a* < *x* < *b*) with the Poisson calculator. You must first calculate P(*x* < *b*), and from this result subtract P(*x* < *a*). Alternatively, you could find P(*x* = *a*), P(*x* = *a* + 1), …, P(*x* = *b*) and total these results.

**Normal Distribution**

The normal calculator in StatCrunch can be accessed through **Stat > Calculators > Normal**. The dialog box asks you to enter μ and σ*.* These are defaulted to 0 and 1 respectively, the parameters for the standard normal (Z) distribution. These can be changed to work with any normal distribution. You also enter an inequality sign: < or >. The calculator calculates the probability and displays a normal curve with the appropriate area shaded.

Should you need to calculate P(*a* < *x* < *b*) you must first calculate P(*x* < *b*) and from this result subtract P(*x* < *a*).

The normal calculator also handles what I call “reverse normal” problems in which you are given a probability and asked to find the value of the random variable associated with it. Simply enter values for the mean and standard deviation, as well as the probability and inequality (left tailed or right tailed). When you click the Compute button, StatCrunch gives you the value of the variable that fits the given situation.

**Ease Of Use**

My students found these calculators very intuitive to use. When I presented them in class I let the students tell me how to enter values in the dialog boxes. They were able to do so with no difficulty.

**Conclusion**

These calculators are powerful and very easy to use. Students still need to understand each distribution, as well as how to tell the difference between them, in order to be successful with StatCrunch. Now, if I could only come up with a way to test them using StatCrunch even though our class does not meet in a computer lab. Any suggestions?

-George

*I am a mathematics instructor at College of the Sequoias in Visalia, CA. I have decided to add technology related articles, including articles based on StatCrunch, to my Thursday blog lineup. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website.*

Entry filed under: Math, StatCrunch, technology. Tags: amatyc, binomial, binomial distribution, binomial probability, george woodbury, ictcm, Math, normal, normal distribution, normal probability, Pearson Education, poisson, poisson distribution, poisson probability, probability, StatCrunch, statistics, stats, teaching, technology, woodbury.

1.Diane | March 11, 2011 at 7:06 amI have been playing with StatCrunch today and can’t figure out a way to find the exact values for the binomial distribution? I get a histogram…can I get a table?

Thanks!

2.georgewoodbury | March 11, 2011 at 7:40 amHi Diane,

You cannot get a table from the calculator.

I wonder if they could add that to the output?