This Java applet demonstrates the use of a normal distribution to approximate a binomial distribution. Correction for continuity is automatically used. The parameters of the binomial can be entered into two entry fields. After pressing enter, the applet computes the binomial probability, the normal approximation and it shows a graph of the normal approximation with correction for continuity. A few exercises are given.
Type of Material:
Simulation.
Recommended Uses:
The applet is excellent as a class demonstration when discussing the normal approximation of a binomial distribution. It may also be used by students to complete independent assignments.
Technical Requirements:
It requires a "Java-enabled" browser.
Identify Major Learning Goals:
This applet demonstrates the relationship of the normal distribution to the binomial distribution. The applet can be used to check the accuracy of this approximation.
Target Student Population:
Students in statistics courses at the high school through undergraduate level.
Prerequisite Knowledge or Skills:
Familiarity with the binomial distribution, normal distribution, and correction for continuity.
Content Quality
Rating:
Strengths:
The applet visually demonstrates the normal approximation when binomial parameters are entered by the user, automatically incorporating the appropriate correction for continuity. The user has the option of ?turning off? the calculations for both the normal approximation and the binomial probability, allowing the opportunity to calculate these values prior to reviewing the answer.
Directions are provided for using the applet to approximate the probability of obtaining any single number of successes. When the user inputs the same number as both the lower and upper values, the correction for continuity is graphed and the approximation is computed.
The applet can be used to see that for values of p not far from 0.5 and for values of N bigger than 20, the normal approximation is good. For values of p close to either 0 or 1 the normal approximation is not so good. The student could use the applet to experimentally discover these results, or the instructor may use the applet to demonstrate them.
Concerns:
Probability is represented by ?p? in the applet and sometimes by in a discussion on the sampling distribution of a proportion. This may be confusing to some users.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Given a range of values by the user, the graph shows the normal approximation with the appropriate continuity correction. The calculations for both the normal approximation and the corresponding binomial probability are quickly reported. The visual representation of the normal approximation is highly effective in demonstrating the use of continuity corrections. The calculations are easy to compare for various values of n and p. This applet is excellent in demonstrating the accuracy of the approximation for various values of n and p.
Concerns:
There are very few exercises. The instructor will need to develop exercises according to the level of the class.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet has very clear instructions. It contains explicit explanations about what the applet does and how it should be used. The order for entering the parameters is not important for the applet as ?from 7 to 5? works just as well as ?from 5 to 7?. Error messages occur when an attempt is made to enter non-integer data.
Concerns:
None
Creative Commons:
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