Normal distribution with 2 equations
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?