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 μ = 2.2 MPa and ( = .9 MPa.
a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa.
b. Find the probability that the tip resistance will exceed 1.0 MPa.
c. Find a value of tip resistance, T, such that 35% of all soil samples have tip resistance values that exceed T.