Quantitative Chemical Analysis
Quantitative Chemical Analysis
9th Edition
ISBN: 9781464135385
Author: Daniel C. Harris
Publisher: W. H. Freeman
Question
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Chapter 4, Problem 4.5P

(a)

Interpretation Introduction

Interpretation:

Using figure 4-1, the fraction of bulbs that is expected to have a lifetime greater than 1005.3 h has to be calculated

Concept Introduction:

Gaussian curve:

The Gaussian curve is given by the formula:

y=1σe(xμ)2/2

Where,

μ is approximated by x¯

σ is approximated by s

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

1/σ is normalization factor.

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

z=xμσxx¯s

To Calculate: The fraction of bulbs that is expected to have a lifetime greater than 1005.3 h using figure 4-1

(b)

Interpretation Introduction

Interpretation:

The fraction of bulb that is expected to have a lifetime between 798.1 and 901.7 h has to be calculated

Concept Introduction:

Gaussian curve:

The Gaussian curve is given by the formula:

y=1σe(xμ)2/2

Where,

μ is approximated by x¯

σ is approximated by s

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

1/σ is normalization factor.

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

z=xμσxx¯s

To Calculate: The fraction of bulb that is expected to have a lifetime between 798.1 and 901.7 h

(c)

Interpretation Introduction

Interpretation:

Using Excel NORMDIST function, the fraction of bulb that is expected to have a lifetime between 800 and 900 h has to be calculated

Concept Introduction:

Gaussian curve:

The Gaussian curve is given by the formula:

y=1σe(xμ)2/2

Where,

μ is approximated by x¯

σ is approximated by s

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

1/σ is normalization factor.

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

z=xμσxx¯s

To Calculate: The fraction of bulb that is expected to have a lifetime between 800 and 900 h using Excel NORMDIST function

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