oblem Helo /4 pointsboBascbtat? 7503 Coal is carried from a mine in a power long

Question

oblem Helo /4 pointsboBascbtat? 7503 Coal is carried from a mine in a power long train. The automatic hopper car loader is set to put 74 tons West Virginia to a power plant in New York in hopper cars on a ded into each car are normally distributed, with mean -74 tons and standard deviation -1.2 ton. a) What is the probability that one car chosen at random will have less than 73.5 tons of coal (Round your answer to four decimal places.) at is the probability that 47 cars chosen at random ill have a mean load weight of less than 73.5 tons of coal? (Round your answer to four decimal places.) (b) Wh (c) Suppose the weight of coal in one car was less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? O Yes O No Suppose the weight of coal in 47 cars selected at random had an average x of less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? O Yes, the probability that this deviation is random is very small. O Yes, the probability that this deviation is random is very large. O No, the probability that this deviation is random is very small. O No, the probability that this deviation is random, is very large. Need Help? Rosdh Tatk to s Tter

Explanation / Answer

Ans:

a)

z=(73.5-74)/1.2=-0.4167

P(X<73.5)=P(z<-0.42)=0.3372

(without round off z value to 2 decimal places,P(X<73.5)=0.3385)

b)standard error of mean=1.2/sqrt(47)=0.175

z=(73.5-74)/0.175=-2.86

P(z<-2.86)=0.0021

c)Yes,as Probabilty of one randomly selected car is high.

d)No,as the probability that this deviation is random is very small.

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