Data has been assigned from 15 concrete cylinders that have had the 28-day compressive strength of concrete determined as required by ASTM specification C39 (ASTM C39 Standard Test Method: Compressive Strength of Cylinders of concrete), refer to the data in Table P2 assigned to each student). With the data, the following must be determined:
a) Average value E[X]
b) Variance and standard deviation, V[X] and V(V[X]), respectively
If you take that the compressive capacity of concrete is a random variable X and fits well to a normal distribution, determine the following:
c) P(X≥ 3000 psi)
d) P(X2 4000 psi)
e) P(X2 5000 psi)
f) P(3500 psi ≤x≤ 4500 psi)

Data in f’c [psi]

Cylinder 1 - 4070
Cylinder 2 -4626
Cylinder 3 - 4483
Cylinder 4 - 4692
Cylinder 5 - 4635
Cylinder 6 - 4823
Cylinder 7 -4873
Cylinder 8- 4224
Cylinder 9 -4166
Cylinder 10 - 4757
Cylinder 11 - 4700
Cylinder 12 - 4336
Cylinder 13 - 4971
Cylinder 14 - 4620
Cylinder 15 - 4646