Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a longtrain. The automatic h...

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Coal is carried from a mine in West Virginia

April 14, 2018

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long
train. The automatic hopper car loader is set to put 73 tons of coal into each car. The actual weights of
coal loaded into each car are normally distributed, with mean ? = 73 tons and standard deviation ? =
1.4 ton.
(a) What is the probability that one car chosen at random will have less than 72.5 tons of coal? (Round
your answer to four decimal places.)

(b) What is the probability that 31 cars chosen at random will have a mean load weight x of less than
72.5 tons of coal? (Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than 72.5 tons. Would that fact make you suspect
that the loader had slipped out of adjustment?
Yes No
Suppose the weight of coal in 31 cars selected at random had an average x of less than 72.5 tons. Would
that fact make you suspect that the loader had slipped out of adjustment? Why?
Yes, the probability that this deviation is random is very small.
Yes, the probability that this deviation is random is very large.
No, the probability that this deviation is random is very small.
No, the probability that this deviation is random is very large.










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