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5. Deep mixing is a ground improvement method developed for soft soils like clay, sitt, and
peat. Swedish 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 =2.2MPa and standard deviation =.9MPa. a. Find the
probability that the tip resistance will fall between 1.3 and 4.0MPa. b. Find the probability that
the tip resistance will exceed 1.0MPa. c. Find a value of tip resistance, T, such that 35% of all
soil samples have tip resistance values that exceed T.

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