-4 points BBUnderStat12 65 013 Notes Ask Your s carried from a mine in West Virg

Question

-4 points BBUnderStat12 65 013 Notes Ask Your s 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 56 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ?-56 tons and standard deviation o 0.5 ton (a) What is the probability that one car chosen at random will have less than 55.5 tons of coal? (Round your answer to four decimal places.) (b) What is the y that 45 cars chosen at random will have a mean load weight x of less than 55.5 tons of coal? (Round your answer to four decimal places.) (e) Suppose the weight of coal in one car was less than 55.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? O Yes No Suppose the weight of coal in 45 cars selected at random had an average x of less than 55.5 tons. Would that fact make you suspect that the loader had slipped out of adjustmers 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.

Explanation / Answer

Sol:

mean=56

sd=0.5

P(X<55.5)

Z=x-mean/sd=55.5-56/0.5

z=-1

P(Z<-1)

=1-P(Z<1)

=1-0.8413

ANSWER=0.1587

USING SOFTWARE ALSO WE CAN FIND ASBELOW

Rcode is:

pnorm(55.5, mean=56, sd=0.5)
0.1586553

sOLUTIONB:

sample sd=popsd/sqrt(n)=0.5/sqrt(45)

pnorm(55.5, mean=56, sd=0.5)

9.851727e-12

ANSWER:0.0000

Solutionc:

YES

since the probability=0.1587

Solutiond:

NO ,the probability that thsi deviaton is random is very small

OPTIONC

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