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Quantitative Techniques – I Tanima Dutta, Lovely Professional University

Notes Unit 15: Normal Probability Distribution

CONTENTS
Objectives

Introduction
15.1 The Conditions of Normality

15.2 Probability Density Function
15.3 Properties of Normal Probability Curve
15.4 Probability of Normal Variate in an Interval

15.5 Normal Approximation to Binominal Distribution
15.6 Normal Approximation to Poisson Distribution
15.7 Summary

15.8 Keywords
15.9 Review Questions
15.10 Further Readings

Objectives

After studying this unit, you will be able to:
Tell about normal probability distribution
Discuss various conditions of normality

State the relevance of Probability Density Function
Explain shape and properties of normal distribution curve
Focus on Fitting a normal curve

Introduction

The normal probability distribution occupies a place of central importance in Modern Statistical
Theory. This distribution was first observed as the normal law of errors by the statisticians of
the eighteenth century. They found that each observation X involves an error term which is
affected by a large number of small but independent chance factors. This implies that an observed
value of X is the sum of its true value and the net effect of a large number of independent errors
which may be positive or negative each with equal probability. The observed distribution of
such a random variable was found to be in close conformity with a continuous curve, which was
termed as the normal curve of errors or simply the normal curve.

Did u know? Since Gauss used this curve to describe the theory of accidental errors of
measurements involved in the calculation of orbits of heavenly bodies, it is also called as
Gaussian curve.

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