At HP Games Imported From IE 11 6.5 013 Coal is carried from a mine in West Virg

Question

At HP Games Imported From IE 11 6.5 013 Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The sutomatic hopper car loader is set to put 6i tons of coal into each car: The actual weights of coal loaded into each car are nornally distributed, with mean -61 tons and standard deviation. 1 1 ton. (a) what is the probability that one car chosen at random will have less than 60.5 tons of coal? (Round your answer to four decimal places.) b) What is the probability that 19 cars chosen at random will have a mean load weight of les than 60 s tons of coal? (Round your answer to four decimal places) (c) Suppose the weight of coal in one car was less than 60.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the welght of coal in 19 cars selected at random had an average of less than do.5 tons, Would that fact make you suspect that the loader had adjustment? Why? Yes, the probability that this devlation is random is very small. yes, the probability that this devlation is random is very large tio, the probability that this deviation is random is very small. No, the probability that this deviation is random is very large.

Explanation / Answer

Formula: Z = (X - mean)/std. dev.

a) P(X < 60.5) = P(Z < (60.5 - 61)/1.1) = P(Z < -0.4545) = 0.3247

b) standard error, se = 1.1/sqrt(19) = 0.252357
P(X_bar < 60.5) = P(Z < (60.5-61)/0.252357) = P(Z < -1.9813) = 0.0238

c) No

d) Option A. The probability that this deviation is random is very small

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