Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Swedish civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns in the journal Giorisk (Vol. 7, 2013). 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 = 2.2 MPa and o = 0.9 MPa. Complete parts a through c below. a. Find the probability that the tip resistance will fall between 1.5 and 3.9 MPa. The probability is .7522 . (Round to four decimal places as needed.) b. Find the probability that the tip resistance will exceed 1.1 MPa. The probability is .8892 . (Round to four decimal places as needed.) c. Find a value of tip resistance, T, such that 20% of all soil samples have tip resistance values that exceed T. T= (Round to two decimal places as needed.)

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.