Chapter 4, Problem 4.8P

Interpretation Introduction

Interpretation:

On repeating the problem 4-7 and using the values $50\text{, 100 and 150}$ for standard deviation, all three curves has to be shown as superimposing on a single graph.

Concept Introduction:

Gaussian curve:

The Gaussian curve is given by the formula:

$y=\frac{\text{1}}{\text{σ}\sqrt{\text{2π}}}{e}^{-{(x-\text{μ)}}^{\text{2}}/{\text{2σ}}^{\text{2}}}$

Where,

$\text{μ}$ is approximated by $\overline{x}$

$\text{σ}$ is approximated by s

e is the base of the natural logarithm $(e=2.71828)$

$1/\text{σ}\sqrt{\text{2π}}$ is normalization factor.

The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:

$z=\frac{x-\text{μ}}{\text{σ}}\approx \frac{x-\overline{x}}{s}$