Graphical calculators for discrete distributions

This tutorial covers how to use StatCrunch calculators for discrete distributions. StatCrunch offers such calculators for the binomial, hypergeometric, and Poisson distributions. These calculators allow for the calculation of a probability given reference value(s). A graphic of the the distribution is provided with highlighted bars corresponding to a user specified probability. In this example, focus will be placed on using the binomial calculator, but the same techniques can be applied to the calculators for other discrete distributions. To begin, load an Empty Data Table after signing in to StatCrunch.

Creating the calculator

All StatCrunch calculators are found under the Stat > Calculators menu. To create a binomial calculator, choose the Stat > Calculators > Binomial menu option. This will load the calculator shown below for a binomial distribution with a total number of trials of 10 and a probability of success of on each trial of 0.5. These parameters defining the binomial distribution can be changed by editing the inputs below the distribution graph. For the binomial calculator below, these inputs are labeled as n (total number of trials) and p (probability of success). The second row of inputs is used to define the probability of interest associated with the distribution. By default, the binomial calculator shows the probability of 5 or fewer successes in red and indicates the probability of this event is 0.62304687.

Finding the associated probability above or below a reference value

A probability associated with another reference value can be easily computed. For example, type 2 for the reference value in the box to the right of the ≤ sign as shown below, and click Compute (or press the *Enter* key). The probability of being less than or equal to 2 is then computed to be 0.0546875. The distribution graph changes to reflect the new reference value with the resulting probability shown in red.

StatCrunch's discrete calculators can also be used to find the probability of a value being ≥, <, >, or = to the reference point. Enter 6 for the reference value, and change the direction selector to > as shown below. Click Compute (or press the *Enter* key) to update the results. The probability of being greater than 6 is then computed to be 0.171875. The distribution graph changes to reflect the new reference value with the resulting probability above this point shown in red.

Computing the probability between two reference values

To find the probability of falling between two reference values, click the Between button in the upper left of the calculator window. This will produce a new graph with the area between the default reference values of 3 and 6 (inclusive) colored in red as shown below. The probability of a value falling between these two values is shown to be 0.7734375.

Change the first reference value to 5 and the second to 7 as shown below. Note the second reference value must be greater than the first one. Press Compute (or press *Enter*) to compute the probability of a value falling between these two reference values as shown below. The values between5 and 7 are shown in red, and the corresponding probability of 0.56835937 is also displayed. Click the Standard button in the top left of the calculator to switch back to the original calculator with only a single reference value.

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