Coal is carried from a mine in West Virginia to a power plant in New York in hop
ID: 3325314 • Letter: C
Question
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 set to put 57 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean -57 tons and standard deviation = 0.7 ton. (a) What is the probability that one car chosen at random will have less than 56.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 18 cars chosen at random will have a mean load weight x of less than 56.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 56.5 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 18 cars selected at random had an average x of less than 56.5 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.Explanation / Answer
Solution:
a) The probability that one car chosen at random will have less than 56.5 tons of coal is
P(X < 56.5) = P(Z < 56.5-57/0.7)
= P(Z < -0.7142)
= 0.2389
b) P(x < 56.5) = P(x-57/(0.718)/ < 56.5-57/(0.7/18))
= P(Z < -3.0305)
= 0.0012
c) Suppose the weight of coal in one car was less than 56.5 tons. I would not suspect that the loader had slipped out of adjustment because the probability of this event happening is 0.2389, which is quite high.The answer is No.
d) Suppose the weight of coal in 18 cars selected at random had an average x of less than 56.5 tons. I would definitely suspect that the loader had slipped out of adjustment, because this probability isquite low. So the answer is, Yes, the probability that this deviation is random is very small.