Given:
μ = 2 min, population mean
σ = 0.5 min, population standard deviation
We want to find P(x>3).
Calculate the z-score
z= (x-μ)/σ = (3-2)/0.5 = 2
From standard tables, obtain
P(x ≤ 3) = P(z ≤ 2) = 0.9772
Therefore
P(x > 3) = P(z > 2) = 1 - 0.9772 = 0.0228
Answer: 0.02275
To answer this item, we take the differential of the equation and equate to zero.
C(x) = 0.8x² - 256x + 25939
Differentiation,
dC(x) = 1.6x - 256
dC(x) = 1.6x - 256 = 0
The value of x from the derived equation above is 160.
Thus, the number of machine to be made in order to minimize the cost should be 160.
Substitute the given values for the parameters in the point-slope form of the equation of a line. That form is
y - k = m(x - h)
for point (h, k) and slope m.
You have (h, k) = (1, 2) and m=-3, so your equation is
y - 2 = -3(x - 1)
