# Normal distribution with 2 equations

• May 27th 2010, 02:36 AM
LordMayor
Normal distribution with 2 equations
Hi Guys,
I'm having trouble with the following Question. I don't know where I should start and what I need to do with the correlation. I hope you can show me a direction to solve this:

The Mayor wishes to build a new tunnel. He has been told that the cost (C) of the tunnel (in billions of dollars) can be estimated by:

C = 1.5 + 0.4 T1

where T1 is the time in years which it takes to build the tunnel. The Mayor has also been told that T1 is a random variable with a normal distribution with a mean of 3 and a standard deviation of 0.6.
Opposition research shows that alternatively a new bridge could be built for cost B:

B = 1.3 + 0.4 T2

where T2 is the time in years which it takes to build the bridge. They have also been told that T2 is a random variable with a normal distribution with a mean of 2.5 and a standard deviation of 0.5.
The times taken to build the tunnel and the bridge have a correlation of 0.8.
What is the probability that the bridge would cost more to build than the tunnel?

Cheers
• May 27th 2010, 02:41 PM
matheagle
You want $P(B-C>0)$

NOW B-C is a normal random variable.
YOUR job is to compute it's mean and variance and calculate that probability above.
I had thought that T1 and T2 would be independent, but they gave you the correlation.
Hence you can compute the their covariance and thus the variance of B-C.