Railroad freight cars filled with coal have weights that are approximately normally distributed with a mean of 72 tons and a standard deviation of 12 tons. A train of 50 coal cars is compiled. The engine assigned to pull the trail can pull a maximum weight of 3,400 tons.
a) What is the probability the engine will be able to pull the train?
b)If one coal car is removed from the train, what is the new probability the engine could pull the train?
c) How many coal cars would have to be removed from the original train of fifty cars to give the engine a 50% chance at pulling the train?

Question

Railroad freight cars filled with coal have weights that are approximately normally distributed with a mean of 72 tons and a standard deviation of 12 tons.  A train of 50 coal cars is compiled.  The engine assigned to pull the trail can pull a maximum weight of 3,400 tons.
a) What is the probability the engine will be able to pull the train?
b)If one coal car is removed from the train, what is the new probability the engine could pull the train?
c) How many coal cars would have to be removed from the original train of fifty cars to give the engine a 50% chance at pulling the train?

anonymous · Answer

My answer so far, the numbers don't seem quite right.
a) p= .0092
b) .068
c) I'm guessing 3, not sure though.