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 is set to pull 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 73 tons and standard deviation ? = 0.9 ton. (a) What is the probability that one car chosen at random will have less than 72.5 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 x of less than 72.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 72.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 19 cars selected at random had an average x of less than 72.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? 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.

Answer 1

Here it is given that the actual weights of coal loaded into each car are normally distributed, with mean = 73 tons and standard deviation = 0.9 ton

a. Now we need to find

As x is normally distributed we can convert x to

So

b. Now we need to find

As population is normally distributed, sample mean is also normally distributed as per central limit theorem

So we can convert

Hence

So

C. No 28.92% probability is not out of range of normal

Yes, the probability that this deviation is random is very small.