### Normal Approximation to Binomial Probability

This applet computes binomial probabilities for ranges of number of events and, if desired, computes and
illustrates the normal approximation to those probabilities. Text boxes allow specification of total number
of events, probability of a "success", and beginning and ending values for the range of number of events
for which the probability is computed. Note that the beginning and ending values may be the same to compute
the probability of a specific number of events *k*. Click on the "Toggle Normal Approximation" button
to turn the display of the normal approximation on and off.

When the page loads, the applet displays the details for Example 7.11 and Figure 7.9. Be sure to click on the "Toggle Normal Approximation" button.

#### Figure 7.8

An example, without numerical values, is displayed in Figure 7.8. The graph below depicts the same representation and provides the numerical values.

#### HTML and Param tags

Below is sample code to place this applet on an html page. The codebase is specified relative to the html file and does not need to be "../../lib" as below.

<applet code="com.bolderstats.normal.BinomialNormalApproximation.class" width="500" height="400" codebase="../../lib" archive="bolderstats_obf.jar,jmsl_obf.jar" > <param name="N" value="20" /> <param name="PROB" value=".5" /> <param name="BEGIN" value="8" /> <param name="END" value="12" /> </applet>

- N
- The total number of trials. Must be between 2 and 54, inclusive. Default is N = 20.
- PROB
- The probability of a "success" on each trial. Default is PROB = 0.5.
- BEGIN
- The beginning number of events for which the probability is to be computed. Default is BEGIN = 8.
- END
- The ending number of events for which the probability is to be computed. Default is END = 12.
- ALLOWNORMAL
- A Boolean value that determines whether the normal appproximation is availabe in the applet. Disallowing the normal approximation converts the applet to a simple calculator for binomial probabilities. The default is TRUE.