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Chapter 2: Q T2.3. (page 149)

Rainwater was collected in water containers at 30different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60and 1.10,respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH unit to all of the values and then multiplying the result by 1.2What are the mean and standard deviation of the corrected pH measurements?

a.5.64,1.44b.5.64,1.32c.5.40,1.44d.5.40,1.32e.5.64,1.20

Short Answer

Expert verified

The correct option is (b)5.64,1.32

Step by step solution

01

Given information

μx=4.60σx=1.10

02

Concept

Properties of mean and standard deviation

μaX+b=aμX+bσaX+b=aσX

03

Calculation

Adding 0.1 to every value and then multiplying this by 1.2

1.2(x+0.1)=1.2x+0.12μ1.2X+0.12=1.2(4.60)+0.12=5.64σ1.2X+0.12=1.2(1.10)=1.32

Hence, the correct option is (b)

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