Normal distribution with 2 equations

May 2010
1
0
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
 

matheagle

MHF Hall of Honor
Feb 2009
2,763
1,146
You want \(\displaystyle P(B-C>0)\)

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.
 
  • Like
Reactions: mr fantastic