Question

Switzerland has lots of tunnels. Too many vehicles in the tunnel can create a hazardous situation. On average the time to pass Gotthard tunnel has mean of 12.1 minutes and standard deviation of 3.8 under ordinary traffic conditions. It is assumed that if the traffic passes the tunnel slower than in 13 minutes, it creates a ventilation problem for the tunnel. If the time is faster than 11 minutes, the movement is too fast and dangerous.

a) For a car what is the chance that it passes through the tunnel in optimal time?

b) If there are 50 cars presently in the tunnel, what would be the chance that they all pass the tunnel on average in optimal time (between 11 and 13 minutes)? Did your answer change from question a)? Explain.

Answer 1