Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercises 2.47 and 2.65 (pp. 96 and 104). Recall that slices of sandstone blocks were measured for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C).

a.Combine the mean (from Exercise 2.47) and standard deviation (from Exercise 2.65) to make a statement about where most of the permeability measurements for Group A sandstone slices will fall. Which rule did you use to make this inference and why?

b.Repeat part afor Group B sandstone slices.

c.Repeat part afor Group C sandstone slices.

d.Based on all your analyses, which type of weathering (type A, B, or C) appears to result in faster decay (i.e., higher permeability measurements)?

Mean from Ex. 47 = 73.62

Standard Deviation from Ex. 65 = 14.48

Minimum = 55.20

Maximum = 122.40

To find the standard deviation where most of the permeability measurements will fall, we will first find k.

$$\begin{gathered} \overline{x}-ks=Max \\ 73.62-k(14.48)=122.40 \\ k(14.48)=122.40-73.62 \\ k(14.48)=48.78 \\ k=\frac{48.78}{14.48} \\ k=3.37 \end{gathered}$$

Therefore, we can say that most of the permeability measurements will fall between 3 standard deviations from mean.

We have used the Chebyshev Rule, because we did not have any information about the distribution of the data. And Chebyshev’s rule allows us to use it on any type of distribution.

Mean from Ex. 47 = 128.54

Standard Deviation from Ex. 65 = 21.97

Minimum = 50.40

Maximum = 150.00

To find the standard deviation where most of the permeability measurements will fall, we will first find k.

$$\begin{gathered} \overline{x}-ks=Max \\ 128.54-k(21.97)=150 \\ k(21.97)=150-128.54 \\ k(21.97)=21.46 \\ k=\frac{21.46}{21.97} \\ k=0.97 \end{gathered}$$

Therefore, we can say that most of the permeability measurements for condition 2 will fall approximately between1 standard deviations from mean.

Mean from Ex. 47 = 83.07

Standard Deviation from Ex. 65 = 20.05

Minimum = 52.20

Maximum = 129.00

To find the standard deviation where most of the permeability measurements will fall, we will first find k.

$$\begin{gathered} \overline{x}-ks=Max \\ 83.07-k(20.05)=129 \\ k(20.05)=129-83.07 \\ k(20.05)=45.93 \\ k=\frac{45.93}{20.05} \\ k=2.29 \end{gathered}$$

Therefore, we can say that most of the permeability measurements for condition 3 will fall between 2 standard deviations from mean.

Sandstone decays faster under Type B weathering, because most of the values in this group fall between 1 standard deviation from mean.