A contractor is interested in the total cost of a project for which he intends to bid. He
estimates that materials will cost P25000 and that his labour will cost P900 per day. The
contractor then formulates the probability distribution for completion time (X), in days, as
given in the following table.
Completion time in days (X) 10 11 12 13 14
P(X=x) 0.1 0.3 0.3 0.2 0.1
a) Determine the total cost function C for the project.
b) Find the mean and variance for completion time X.
c) Find the mean, variance and standard deviation for the total cost C
cost = 25000 + .1(10)(900) + .3(11)(900) + .3(12)(900) + ... + .1(14)(900)
= ....
not sure what methods your text or your course suggests to find the mean and variance
a) To determine the total cost function C for the project, you need to multiply the estimated labor cost per day by the number of days of completion time (X), and then add the material cost:
C(X) = (labor cost per day) * X + (material cost)
Given that the labor cost per day is P900 and the material cost is P25000, the total cost function becomes:
C(X) = 900X + 25000
b) To find the mean and variance for completion time X, you need to calculate the expected value and the variance using the probability distribution table provided.
Mean (Expected Value):
The mean (μ) for completion time X is calculated by multiplying the completion time values (X) by their respective probabilities (P(X=x)), and then summing them up:
μ = Σ (X * P(X=x))
μ = 10 * 0.1 + 11 * 0.3 + 12 * 0.3 + 13 * 0.2 + 14 * 0.1
Variance:
The variance (σ^2) for completion time X is calculated by finding the squared difference between each completion time value (X) and the mean (μ), multiplying it by their respective probabilities (P(X=x)), and summing them up:
σ^2 = Σ [(X - μ)^2 * P(X=x)]
σ^2 = [(10 - μ)^2 * 0.1] + [(11 - μ)^2 * 0.3] + [(12 - μ)^2 * 0.3] + [(13 - μ)^2 * 0.2] + [(14 - μ)^2 * 0.1]
c) To find the mean, variance, and standard deviation for the total cost C, you need to use the mean and variance values obtained from part b, and apply them to the total cost function.
Mean:
The mean (μ_c) for the total cost C can be found by substituting the mean (μ) for completion time X into the total cost function:
μ_c = C(μ)
μ_c = 900 *μ + 25000
Variance:
The variance (σ_c^2) for the total cost C is calculated by substituting the variance (σ^2) for completion time X into the total cost function:
σ_c^2 = [900^2 * σ^2]
Standard Deviation:
The standard deviation (σ_c) for the total cost C is the square root of the variance (σ_c^2):
σ_c = √(σ_c^2)
Now you have the formulas to calculate the mean, variance, and standard deviation for the total cost C using the known values from the problem statement.