Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 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 units to all of the values and then multiply the result by 1.2. Find the mean and standard deviation of the corrected pH measurements.

Question

Physics

Mercedes Ferguson

Yesterday, 15:13

Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 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 units to all of the values and then multiply the result by 1.2. Find the mean and standard deviation of the corrected pH measurements.

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Damon Mathis · Answer 1

The standard deviation of corrected pH is

5.64, 1.32

Explanation:

To find the measurements pH given

μx = 4.60, σx = 1.10

So using the measurement as a pH

μₐX + b = aμ X + b

μ1.2 x + 0.12

1.2 (4.60) + 0.12 = 5.64

σₐX + b = a σ X

σ 1.2 X + 0.12

1.2 (1.10) = 1.32