Will Steve the train engineer be mad?

Question

This is a basic $Z$- score question. I would just like to know if I solved it correctly.

Train cars for the Crandic Railway Company carry $25$ standard-sized containers. The weight of each container is described by a distribution with a mean of $380$ pounds and a standard deviation of $50$ pounds. Steve, the train engineer, becomes upset if a train car contains more than $10,000$ pounds. What fraction of train cars would make him angry.

Mean of a train car $= 25 \cdot 380 = 9500$

SE for a train Car $= (25 \cdot 50) / \sqrt{50} = 250$

$(9500 - 10000) / 250 = 2$

$1-(Z \leq 2) = 1-0.9772 = 0.0228$

$2.28\%$ of train cars will make Steve angry..

Thank you for you help.

Answer 1

Note that a train contains more than 10000 pounds if and only if it is more than 2 standard deviations to the high side of the average. So the answer is approximately 1.35%