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Coal is carried from a mine in West Virginia to a power plant in New York...

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Statistics

Coal is carried from a mine in West Virginia to a power plant inNew York in hopper cars on a long train.

The automatic hopper car loader is set to put 71 tons of coalinto each car.

The actual weights of coal loaded into each car are normallydistributed, with mean μ = 71 tons and standarddeviation σ = 0.5 ton.

(a) What is the probability that one car chosen at random willhave less than 70.5 tons of coal? (Round your answer to fourdecimal places.)


(b) What is the probability that 24 cars chosen at random will havea mean load weight x of less than 70.5 tons of coal?(Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 70.5 tons.Would that fact make you suspect that the loader had slipped out ofadjustment?

Yes or No   


Suppose the weight of coal in 24 cars selected at random had anaverage x of less than 70.5 tons. Would that fact make yoususpect that the loader had slipped out of adjustment? Why?

a. Yes, the probability that this deviation is random is verysmall.

b. Yes, the probability that this deviation is random is verylarge.    

c. No, the probability that this deviation is random is verysmall.

d. No, the probability that this deviation is random is verylarge.

Answer & Explanation Solved by verified expert
3.6 Ratings (647 Votes)
aLet X denote the actual    See Answer
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