Answer:
P(X > 0.418) = 0.27425
Step-by-step explanation:
We are given;
Population mean; μ = 0.4 inch
Variance; Var = 0.0009
Sample mean; x¯ = 0.418
First of all let's get the standard deviation which is;
σ = √Var
σ = √0.0009
σ = 0.03
Now, z - score formula is;
z = (x¯ - μ)/σ
z = (0.418 - 0.4)/0.03
z = 0.6
We want to find the probability that the diameter of a randomly selected pipe will exceed 0.418 inch. Thus;
P(X > 0.418) = 1 - P(X ≤ 0.418)
From z-distribution table attached, P(X ≤ 0.418) = P(Z) = 0.72575
Thus;
P(X > 0.418) = 1 - 0.72575
P(X > 0.418) = 0.27425
