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Lostsunrise [7]
3 years ago
11

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 muμequals=2.72.7 MPa and sigmaσequals=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) = ____

b. Find the probability that the tip resistance will exceed 1.0 MPa.
P (x > 1) = ____

c. Find a value of tip​ resistance, T, such that 36​% of all soil samples have tip resistance values that exceed T.
T = ____
Mathematics
1 answer:
Kitty [74]3 years ago
5 0

Answer:

a)  0.9078

b) 0.9832

c) T = 2.9867

Step-by-step explanation:

Given:-

T  ~ N (2.7 , 0.8 )

Find:

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

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

Find a value of tip​ resistance, T, such that 36​% of all soil samples have tip resistance values that exceed T

Solution:

a) To find the P ( 1.3 < x < 4.0 ) we will first compute the z-score values:

        P (1.3 < x < 4.0 ) = P ( (1.3 - 2.7)/0.8 < Z < (4.0 - 2.7)/0.8)

        P (1.3 < x < 4.0 ) = P ( -1.75 < Z < 1.625)

- Using the Z-table values we can evaluate the probability:

       P (1.3 < x < 4.0 ) = P ( -1.75 < Z < 1.625) = 0.9078

b) To find the P ( x > 1 ) we will first compute the z-score values:

        P ( x > 1.0 ) = P ( Z > (1.0 - 2.7)/0.8)

        P ( x > 1.0 ) = P ( Z > -2.125)

- Using the Z-table values we can evaluate the probability:

       P ( x > 1.0 ) = P ( Z > -2.125) = 0.9832

c) To find the P ( x > T ) we will first compute the z-score values:

       P ( x > T ) = P ( Z > (T - 2.7)/0.8) = 0.36

  - We will search for the z value with the condition above from Z-table.

       P ( Z > (T - 2.7)/0.8) = 0.36,  Z = 0.358375

  - Hence, we calculate for T:

        T = 0.358375*0.8 + 2.7

        T = 2.9867

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agasfer [191]
Okay so, togo flies 30 miles in 3/5 of an hour with the wind.togo flies 30 miles in 5/6 of an hour against the wind. his rate of speed with the wind was 30 / (3/5) = 30*5/3 = 150/3 = 50 mph.his rate of speed against the wind was 30 / (5/6) = 30*6/5 = 6*6 = 36 mph.3/5 of an hour times 50 mph = 30 miles.
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his rate of speed then was the airplane speed plus the wind speed.coming back he was against the wind.his rate of speed then was the airplane speed minus the wind speed.-----50 mph = A + W36 mph = A - W-----looks like A + W - (A - W) should equal 50 - 36.removing parentheses, equation becomesA + W - A + W = 14.
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answer is W = 7 and A = 43.
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