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Komok [63]
3 years ago
11

A sample of lake water was analyzed to determine the amount of metals found in the lake. The standard deviation of the sampling

method was found to be ±6.0%±6.0% . The standard deviation of the analytical method used to determine the amount of metals in the sample was determined to be ±2.4%±2.4% . What is the overall standard deviation?
Chemistry
1 answer:
Sauron [17]3 years ago
8 0

Answer:

The overall standard deviation, s = 6.46 %

Given:

Sampling variance, s_{b} = \pm 6.0% = 0.06

Analytical variance, s_{a} = \pm 2.4% = 0.024

Solution:

Variance additive is given by:

s^{2} = s_{a}^{2} + s_{b}^{2}                        (1)

where

s = overall variance

Also, we know that:

Standard Deviation, \sigma = \sqrt{variance}

Therefore the standard deviation of the sampling, analytical and overall sampling is given by taking the square root of eqn (1) on both the sides:

s = \sqrt{s_{a}^{2} + s_{b}^{2}}

s = \sqrt{0.024^{2} + 0.06^{2}} = 0.0646

s = 6.46 %

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