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Chapter 2: Q. 3 (page 138)

T2.3. Rainwater was collected in water collectors 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 0.1pHunits to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

(a)5.64,1.44

(b)5.64,1.32

(c)5.40,1.44

(d)5.40,1.32

(e)5.64,1.20

Short Answer

Expert verified

The mean and standard deviation of the corrected pH measurements are(b)5.64,1.32.

Step by step solution

01

Given Information

Given:

Number of sites=30

Mean value=4.60

Standard deviation value=1.10

Adding pH=0.1pH

02

Explanation

Given:

μX=4.60

σX=1.10

Add 0.1to every value and then multiply by :

1.2(X+0.1)=1.2X+0.12

Properties mean and standard deviation:

μax+b=aμX+b

σaX+b=aσX

Find the mean and standard deviation for 1.2X+0.12:

localid="1649415494484" μ1.2X+0.12=1.2μX+0.12=1.2(4.60)+0.12=5.64

localid="1649415506162" σ1.2X+0.12=1.2σX=1.2(1.10)=1.32.

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