Chapter 2, Problem 3PT

To determine

To select: the best answer for the given question.

Answer to Problem 3PT

Option D is the correct option.

Explanation of Solution

Given:

The mean and standard deviation of the values are 4.60 and 1.10

Calculation:

It is given that the mean and standard deviation of the amount of acidity in rainwater is 4.60 and1.10 respectively.

  $\mu =4.60,\sigma =1.1$

The error in $\text{pH}$ meter can be corrected by adding $0.1\text{pH}$ units to all of the values and then multiplying the result by 1.2

It is known that mean is not independent of change of origin and scale. Therefore, mean of the corrected pH measurement.

  $(\mu +0.1)\times 1.2=(4.60+0.1)\times 1.2=5.64$

Also, standard deviation is independent of change of origin but not of scale. Therefore, standard deviation of the corrected pH measurement,

  $\begin{array}{l}=\sigma \times 1.2\hfill \\ =1.10\times 1.2\hfill \\ =1.32\hfill \end{array}$

Hence, the mean and standard deviation of the corrected pH measurements are 5.64 and 1.32

Option D is the correct option.

Conclusion:

Therefore, option D is the correct option.