A contractor is interested in the total cost of a project on which he intends to bid. He estimates that materials will cost rs 25,000 and that his labour will be rs900 per day. If he the project takes X days to complete,the total cost of the project (in rupees) will be given as:

c=25,000+900x

there is a table which gives the completion time, in days, for theproject.

Completion time X (days) : Probability
10 : 0.1
11 : 0.3
12 : 0.3
13 : 0.2
14 : 0.1

Find the mean and variance for completion time X.
For mean which is E(x) : i got 11.9
Variance V(x): i got 176.7

standard deviation (x), i got 5.92

Now find the mean and variance for total cost C.
C=25,000+900x

Mean= c=25000 +900x
E(c)=E(25000+900)
=(25000+ 900 v(x)
25000 + 900x
E(x) =11.9
=25000+900 x 11.9
=357,10

but am having problem to find the variance??

help pls!

To find the variance for the total cost C, you can use the formula for the variance of a function of a random variable. In this case, the function is C = 25,000 + 900X, where X is the completion time in days.

The variance, denoted as Var(C), can be calculated as follows:

Var(C) = Var(25,000 + 900X)

Since Var(aX) = a^2 * Var(X) for any constant 'a', we can rewrite the variance as:

Var(C) = 900^2 * Var(X)

Now, let's find the variance of X. The variance of X, denoted as Var(X), is given by:

Var(X) = Σ (x - E(X))^2 * P(x)

where Σ denotes the sum of the terms, x represents the completion time in days, E(X) is the expected value (mean) of X, and P(x) is the probability of X taking the value x.

Using the given completion time values and probabilities, we can calculate Var(X) as follows:

Var(X) = (10 - 11.9)^2 * 0.1 + (11 - 11.9)^2 * 0.3 + (12 - 11.9)^2 * 0.3 + (13 - 11.9)^2 * 0.2 + (14 - 11.9)^2 * 0.1

Simplifying this calculation, we get:

Var(X) = 0.01 * 0.1 + 0.01 * 0.3 + 0.01 * 0.3 + 0.01 * 0.2 + 0.01 * 0.1

Var(X) = 0.001 + 0.003 + 0.003 + 0.002 + 0.001

Var(X) = 0.01

Now, substituting this value back into the equation for Var(C), we have:

Var(C) = 900^2 * 0.01

Var(C) = 810,000

Therefore, the variance for the total cost C is 810,000 rupees.