A wire manufacturing company has inspectors to examine the wire
for fractures as it comes out of a machine. The number of fractures
is distributed in accordance with a Poisson process, having one
fracture on the average for every 60 meters of wire. One day an
inspector has to take an emergency phone call and is missing from
his work for ten minutes.
If the machine turns out 7 meters of wire per minute, what is
the probability that the inspector will miss more than one
fracture?
When the inspector returns to his work, what is the probability
that the next fracture occurs in the next 10 minutes?
What are the expected time and standard deviation of the time
of the first fracture?