Question

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

mu

μ=2.42.4

MPa and

sigma

σ=0.80.8

MPa. Complete parts a through c.

a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa.

​P(1.3≤x≤​4.0)=0.8934

​(Round to four decimal places as​ needed.)

b. Find the probability that the tip resistance will exceed 1.0 MPa.

​P(x>​1)=0.9599

​(Round to four decimal places as​ needed.)

c. Find a value of tip​ resistance, T, such that

39​% of all soil samples have tip resistance values that exceed T.

Answer 1

Ans: Given data, M = 2.4, T = 0.8 a) P (1.3 <x540) P ( 1.3 -2.4 1.3-2.4 X-M 4.0-2.4 s 4 0.8 0.8 P(-1,375 € 26 2) = P(292)-8 (22-.375) values 0.97725 - 0.084566 0.8927 from 2-table] 8 (x> 1) = PL 1-24 X-M 4 ) 0.8 P[2>-1.75) - 1-P125-1.75) I 1-0.04006 = 10.9599 = 0.39 P/x+) - 0,34 P(x > T-24 ) - 0.39 -) 8/23 7-24) - from 2-table P (25 0.27) = 0.39 T= (0.8 x 0.27) + 2.4 T-2.4 0.27 =) 0.8 = 2.616 2.616