Binomial Probability Distribution

Binomial Probability Distributions

A WebQuest for Math 153 (Introduction to Statistical Methods )

Designed by

Donna Hiestand-Tupper
dtupper@ccbcmd.edu

Introduction

Life is usually a very complicated place. There are lots of choices and decisions to be made, which in turn lead to more choices and decisions to be made. However, there are these rare moments in life when you are left with only two choices. For example, tossing a coin results in either "Heads" or "Tails"; recognizing the McDonald's golden arches "Yes" or "No"; "True/False" test are all examples of situations where there are only two possible outcomes.

For an experiment to be a binomial experiment, it must satisfy the four following conditions:

There are only 2 possible outcomes, success or failure;
There are a fixed number of trials, which we call n;
Each trial is independent of any other trail;
The probability remains constant from one trial to the next.

In this chapter, we looked at various binomial situations and determined the probability of success for the given experiment. This webquest will involving searching the National Center for Health Statistics website and examining the probabilities associated that a childs playmates at the local day care center have had their shots.

The Task

At The National Center for Health Statistics website, URL http://www.cdc.gov/nchs/data/hus/hus04trend.pdf#073, there is data on the percentage of "Vaccination coverage among children 19 - 35 months of age according to geographic division, State, and selected urban areas". This is table 73, on page 186 of 427 pages in the pdf document.

You are looking at moving to one of two predetermined urban communities. As part of your research, you are looking for at a nursery school in both cities you are considering moving to. For each city, the nursery school has a limit of 10 children per class. To reduce sibling rivalry, none of the children are related to any other child in the class.

The Process

*Please be advised that this is a very, very long download if you are using a dial-up internet connection. You may prefer going on campus to download the one page you need.

Step 1: Randomly select any two of the major urban areas listed on page 186 of the pdf document from any two different geographic regions. There are 28 cities to chose from. Do NOT choose cities with the same probability of success.

The eight regions you can choose from are New England, Middle Atlantic, East North Central, South Atlantic, East South Central, West South Central, Mountain and Pacific. Please use only the year 2003.

Step 2. Determine whether or not this is a binomial experiment.

Condition	Yes/No	Single sentence for justification (e.g. the number of trials, the probability of success, list possible outcomes, determine independence or dependence)
Fixed Number of Trials
Probability Remains Constant
Two possible outcomes
Each Trial Independent

Step 3: Use Statdisk to create the probability distribution for each city you chose. The Statdisk printout must be submitted with the assignment.

Step 4: Confirm the results found in step three by using the binompdf command on your TI-83. Round these answer to the appropriate number of significant digits.

x	P(x)
0
1
2
3
4
5
6
7
8
9
10

Step 5: Use Statdisk to determine the mean and standard deviation for the percentage of children vaccinated in the study.

Step 6: Use the TI-83 to confirm the results found by Statdisk. Show both the formula and all related work.

Step 7: For both cities, determine each of the following:

P(x > 6) =
P(x < 9) =
The probability that "at least" 4 are immunized?
The probability that "at most 7" are immunized?

Evaluation

You are required to answer each of the above questions. When grading your web assignment, I will be using the rubric below. Each category (calculation, use of technology, theory and written responses) is worth 25 points. The number of points you get per category is based on the ratings excellent, good, acceptable, poor or blank. Use the rubric below as a self-check before turning in your assignment.

	Excellent 1 (25 Points)	Good 2 (20 Points)	Adequate 3 (15 Points)	Poor 4 (10 Points)	Blank 5 (0 Points)
Calculations	No calculation or roundoff errors are present.	Roundoff errors are present.	Calculation errors present.	Calculation and roundoff errors were made.	No Calculations Shown
Use of Technology	Shows complete and appropriate use of Statdisk & TI.	Shows appropriate use of Statdisk & TI, but a calculation error is present.	Limited or inappropriate use of Statdisk or TI.	No use of Statdisk, but TI-83 was used.	No use of Technology evident.
Theory Comprehension	Shows complete comprehension of the Statistical Theory.	Understands most of the theory, however minor errors made.	Shows some understanding of the theory, however explanations are unclear.	Shows limited understanding of the theory.	No understanding of theory evident.
Written Responses	Well written. Neat, typed. No grammatical or spelling errors.	Ideas clearly presented, but spelling or grammatical errors are present.	Poorly written response. Many spelling or grammatical errors present.	Poorly written response. Many spelling or grammatical errors present. Assignment is hand written.	Questions left blank.

Conclusion

Looking at data from the real world can be quite challenging. Had we examined data from a national perspective instead of a regional perspective, the result would not have been a binomial experiment. Race, region of the nation and income level all affect whether or not a child has been immunized.

Last updated on February 14, 2005. Based on a template from The WebQuest Page