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 put58tons of coal into each car. The actual weights of coal loaded into each car arenormally distributed, with mean=58tons and standard deviation=0.5ton.

(a) What is the probability that one car chosen at random will have less than57.5tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that47cars chosen at random will have a mean load weightxof less than57.5tons of coal? (Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than57.5tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes

No

Suppose the weight of coal in47cars selected at random had an averagexof less than57.5tons. 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.