Question

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.

Answer 1

Solution :

a) The total cost function is given as follows :

C = 25000 + 900.X

Where, C is total cost and X is completion time in number of days.

b) The mean of the completion time is given as follows :

The variance of the completion time is given as follows :

We have, E(X) = 11.9

Now,

c) If X is a random variable and C = a + bX, where a and b are two constants then,

E(C) = a + bE(X)

Var(C) = b² Var(X)

We have, C = 25000 + 900X, E(X) = 11.9 and Var(X) = 1.29

Hence,

E(C) = 25000 + (900 × 11.9) = 35710

The mean of the total cost is P35710.

Var(C) = (900)² × 1.29

Var(C) = 1044900

The standard deviation of the total cost is P1022.20.