The Normal Curve As The Limiting Form Of The Binomial Distribution

Author

Joseph Robert Phillips, Prairie View Agricultural and Mechanical College

Date of Award

8-1955

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

Normal distributions are very useful as mathematical models for many frequency distributions found in nature and industry. Thus, a great many measurements made on manufactured articles possess distributions that can be approximated well by normal distributions, true of many biological measurements. The same is also Even if there were few natural distributions of this form, the normal distribution would still be extremely important because of its place in theoretical work. As may be readily inferred, there are many curves which are like the normal curve in that they have at most one mode but differ from the normal curve in that they are not symmetrical. Most of these types of curves are presented by the various graphs obtained by plotting the terms of the expansion of the binomial (p+q= 1/2), Such curves are often referred to as skew curves. where to represents the probability of the occurrence of a certain event, q the probability of its failure, and the number of trials. Lest one should think that the graphs of the terms of the expansion would be rectangular histograms, it is well to say that it is the frequency curve which corresponds to these histograms to which we refer as representative types of frequency curves, When, as a special case, p=q=1/2, the corresponding graph is symmetrical - that is, skewness is absent or zero - and is essentially a form of the normal curve, mathematical justification of this statement, is the writer's purpose for To show the mathematical this investigation and writing this thesis.

Committee Chair/Advisor

E. Haskins

Committee Member

Emma C. Green

Publisher

Prairie View Agricultural and Mechanical College

Rights

Date of Digitization

12/09/2021

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Phillips, J. R. (1955). The Normal Curve As The Limiting Form Of The Binomial Distribution. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/832