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 put 85 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 85 tons and standard deviation σ = 1.8 ton.

(a) What is the probability that one car chosen at random will have less than 84.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 42 cars chosen at random will have a mean load weight x of less than 84.5 tons of coal? (Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than 84.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 42 cars selected at random had an average x of less than 84.5 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

Given = 85, = 1.8

To find the probability, we need the z scores. Z = (X - ) / [ / sqrt(n)]

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(a) n = 1. To find P(X < 84.5)

Z = (84.5 - 95) / 1.8 = -0.28

The required probability = 0.3897

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(b) n = 42. To find P(X < 84.5)

Z = (84.5 - 95) / [1.8 / sqrt(42)] = -1.8

The required probability = 0.0359

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(c) No, because around 39% of the cars will have weights which is less than 84.5 tons.

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(d) Yes, the probability that this deviation is random is very small (< 5%)

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