Question

High-strength concrete is supposed to have a compressive strength greater than 6,000 pounds per square inch (psi). A certain type of concrete has a mean compressive strength of 7,000 psi, but due to variability in the mixing process it has a standard deviation of 420 psi, assuming a normal distribution.

Answer 1

given,

greater compressive strength = 6,000 psi

mean compressive strength(μ) = 7000 psi

standard deviation (σ) = 420 psi

P(X < 6000)

`Z = (x-\mu)/(\sigma)`

`Z = (6000-(7000))/(420)`

Z = - 2.38

P(Z<-2.38) = Area to left - 2.38

from Z table

P(X < 6000) = P(Z<-2.38) = 0.0087

P(fail) = P(X< 6000) = 0.0087 = 0.87