### Topic: Ground Improvement Techniques Using Deep Mixing**Introduction to Deep Mixing:**Deep mixing is a ground improvement method especially developed for enhancing the properties of soft soils like clay, silt, and peat. Civil engineers employ this technique to stabilize soil by mixing it with materials, such as lime-cement columns. **Methodology:**In an investigational experiment, the mixed soil's properties were evaluated by driving a cylindrical rod with a cone tip into the soil. This process, termed as cone penetrometer testing, measures the cone tip resistance in megapascals (MPa). **Statistical Analysis:**The experiment revealed that the tip resistance for the deep-mixed soil followed a normal distribution characterized by a mean (\( \mu \)) of 1.7 MPa and a standard deviation (\( \sigma \)) of 1.1 MPa. ### Exercises:Complete the following parts based on the provided distribution:**Part a: Probability Calculation for Tip Resistance**- Calculate the probability that the tip resistance will fall between 1.3 and 4.0 MPa. \[ P(1.3 \leq X \leq 4.0) = 0.6236 \text{ (Round to four decimal places as needed.)} \]**Part b: Probability Calculation for Exceeding Tip Resistance**- Calculate the probability that the tip resistance will exceed 1.0 MPa. \[ P(X > 1) = \quad \text{(Round to four decimal places as needed.)} \]**Diagrams and Graphs:**There is no specific graphical representation provided in the text; however, the problem involves understanding the normal distribution curve with the specified mean and standard deviation. Typically, such a curve would be bell-shaped, with the highest point at the mean (1.7 MPa) and probabilities tapering off symmetrically on either side. **Conclusion:**Understanding the statistical nature and behavior of soil properties using methods like deep mixing and cone penetration testing is fundamental for civil engineering applications. These exercises help in cementing comprehension of normal distribution and its application in real-world scenarios.For further practice and comprehension, students are encouraged to graph the distribution and visually analyze the probabilities.

We have to find given probability..

Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns. The mixed soil was tested by advancing a cylindrical rod with a cone tip down into the soil. During penetration, the cone penetrometer measures the cone tip resistance (megapascals, MPa). The researchers established that tip resistance for the deep mixed soil followed a normal distribution with u=1.7 MPa and a = 1.1 MPa. Complete parts a through c. a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa. P(1.3sxS4.0) = 0.6236 (Round to four decimal places as needed.) b. Find the probability that the tip resistance will exceed 1.0 MPa. P(x> 1) = (Round four decimal places as needed.)

Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns. The mixed soil was tested by advancing a cylindrical rod with a cone tip down into the soil. During penetration, the cone penetrometer measures the cone tip resistance (megapascals, MPa). The researchers established that tip resistance for the deep mixed soil followed a normal distribution with u=1.7 MPa and a = 1.1 MPa. Complete parts a through c. a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa. P(1.3sxS4.0) = 0.6236 (Round to four decimal places as needed.) b. Find the probability that the tip resistance will exceed 1.0 MPa. P(x> 1) = (Round four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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