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
