Peer Review

Normal Approximation to the Binomial Distribution

Material Detail page

Reviewed:: Mar 23, 2010 by Statistics

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Ratings

Overall Rating:

Content Quality:

Effectiveness:

Ease of Use:

Overview:: This material is part of the broader collection of materials in the Rice Virtual Labs in Statistics by David Lane. The page includes an applet along with text instructions and explanations, links and exercises. The applet provides a graphical calculator of binomial probabilities based on the normal approximation to the binomial. The user can enter values of n and p and a graphical representation of the binomial probabilities will appear with a normal distribution superimposed over it. The user can also enter two endpoints. The applet will then shade the probability between those endpoints (along with the continuity correction). The applet also gives the probability based on the binomial distribution and the probability based on the normal approximation The explanations discuss the Central Limit Theorem and the Correction for Continuity. The exercises are simple text and do not have solutions.
Type of Material:: Java Applet
Recommended Uses:: The applet should be used by individual students when learning the binomial distribution and how to calculate probabilities from a binomial distribution. It is good to use as a precursor to hypothesis testing about a proportion.
Technical Requirements:: Java enabled browser
Identify Major Learning Goals:: This material may help students to learn the following: 1. Describe the relationship between the binomial distribution and the normal distribution. Also point out when (what values of n and p) the normal approximation will not do a good job of approximating the binomial distribution. 2. Describe the continuity correction for a binomial distribution.
Target Student Population:: Introductory statistics students.
Prerequisite Knowledge or Skills:: A basic understanding of probability, the binomial distribution, and the normal distribution.

Content Quality

Rating:
Strengths:: Nice graphical representation of the probability being estimated. Good definition of the central limit theorem and discussion about the continuity correction with an example. Provides a reasonable presentation of the binomial approximation.
Concerns:: The material uses capital "N" for the sample size which may not align with the more typical "n" that is used in most statistics textbooks. The supporting materials also use "M" for the mean of a population which may confuse some students. It would be helpful to see more exercises illustrating when the approximation is appropriate.

Potential Effectiveness as a Teaching Tool

Rating:
Strengths:: This material does a reasonable job of graphically presenting the binomial approximation.
Concerns:: The main weakness of this material is age. It was created many years ago and has some features that are clearly dated. The supporting materials provide exercises that are simply text. They lack interactivity or even answers. The questions themselves do not necessarily encourage the students to use the applet component of the calculator. For instance the exercises include this question: "1. Two equally matched baseball teams play six games. What is the probability that each will win three games?". There is nothing inherent in this question that would drive a student to use the applet or even the normal approximation to the binomial. Another question asks: "4. What is the relationship between N and how well the normal distribution approximates the binomial distribution." (sic) This question does not lead the student to experiment with the applet to discover the relationship. This question could be greatly improved by giving students several values of N to experiment with, then asking them to summarize the result. It should also be noted when it is appropriate to use the normal approximation to do binomial probabilities.

Ease of Use for Both Students and Faculty

Rating:
Strengths:: This applet has very clear instructions and it is very easy to use. The item is visually engaging and interactive.
Concerns:: This applet presents in a rather small form that is to be expected given the age of the applet. It is readable by a person sitting at a computer monitor but it would be difficult to use for classroom presentation on a large overhead projector. The applet also has a problem in that the upper line of text is obscured by the window border. This occurred for the reviewer in both Mozilla and Internet Explorer on a PC.

Other Issues and Comments:: Users note: the maximum value of n appears to be unlimited but the graphing feature fails after n=1020. The links do not take the user to any other websites. It appears that this applet needs to be updated. The version of Internet explorer recommended for Window users is version 4 (no mention to Firefox). The lines for the graph will often go above the actual curve, which takes away from graphical presentation.
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