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Concept explainers
(a)
Interpretation:
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval has to be calculated.
Concept Introduction:
Gaussian curve:
The Gaussian curve is given by the formula:
Where,
e is the base of the natural logarithm
The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:
The area under the whole curve from
To Calculate: Using Table 4-1, the fraction of a Gaussian population that lies within the given interval
(a)
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Answer to Problem 4.2P
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is
Explanation of Solution
Given Interval:
Calculation of Gaussian Population:
The given interval
From the table 4-1, we know that the area from
Similarly, the area from
Therefore, the total area from
Hence, the fraction of a Gaussian population is
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is calculated as
(b)
Interpretation:
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval has to be calculated.
Concept Introduction:
Gaussian curve:
The Gaussian curve is given by the formula:
Where,
e is the base of the natural logarithm
The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:
The area under the whole curve from
To Calculate: Using Table 4-1, the fraction of a Gaussian population that lies within the given interval
(b)
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Answer to Problem 4.2P
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is
Explanation of Solution
Given Interval:
Calculation of Gaussian Population:
The given interval
From the table 4-1, we know that the area from
Similarly, the area from
Therefore, the total area from
Hence, the fraction of a Gaussian population is
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is calculated as
(c)
Interpretation:
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval has to be calculated.
Concept Introduction:
Gaussian curve:
The Gaussian curve is given by the formula:
Where,
e is the base of the natural logarithm
The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:
The area under the whole curve from
To Calculate: Using Table 4-1, the fraction of a Gaussian population that lies within the given interval
(c)
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Answer to Problem 4.2P
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is
Explanation of Solution
Given Interval:
Calculation of Gaussian Population:
The given interval
From the table 4-1, we know that the area from
Therefore, the total area from
Hence, the fraction of a Gaussian population is
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is calculated as
(d)
Interpretation:
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval has to be calculated.
Concept Introduction:
Gaussian curve:
The Gaussian curve is given by the formula:
Where,
e is the base of the natural logarithm
The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:
The area under the whole curve from
To Calculate: Using Table 4-1, the fraction of a Gaussian population that lies within the given interval
(d)
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Answer to Problem 4.2P
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is
Explanation of Solution
Given Interval:
Calculation of Gaussian Population:
The given interval
From the table 4-1, we know that the area from
Therefore, the total area from
Hence, the fraction of a Gaussian population is
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is calculated as
(e)
Interpretation:
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval has to be calculated.
Concept Introduction:
Gaussian curve:
The Gaussian curve is given by the formula:
Where,
e is the base of the natural logarithm
The deviations from mean value is expressed in multiples, z, of the standard deviation and which is given as follows:
The area under the whole curve from
To Calculate: Using Table 4-1, the fraction of a Gaussian population that lies within the given interval
(e)
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Answer to Problem 4.2P
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is
Explanation of Solution
Given Interval:
Calculation of Gaussian Population:
The given interval
From the table 4-1, we know that the area from
The area from
Therefore, the total area from
Hence, the fraction of a Gaussian population is
Using Table 4-1, the fraction of a Gaussian population that lies within the given interval is calculated as
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Chapter 4 Solutions
Quantitative Chemical Analysis 9e And Sapling Advanced Single Course For Analytical Chemistry (access Card)
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