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 69 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 69 tons and standard deviation σ = 0.9 ton. What is the probability that one car chosen at random will have less than 68.5 tons of coal?

Question

Mathematics

Levi Adkins

14 January, 00:33

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 69 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 69 tons and standard deviation σ = 0.9 ton. What is the probability that one car chosen at random will have less than 68.5 tons of coal?

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German Short · Answer 1

0.2839 = 28.93%

Step-by-step explanation:

In order to find find the probability that one car chosen at random will have less than 68.5 tons of coal, we have to find z

Le x be tons of coal in a car

Z = (x - mean) / standard deviation

Z = (x - μ) / σ

P (x<68.5) = P (z < (68.5-69) / 0.9)

P (x<68.5) = P (z < - 0.5555)

Then we use the z table to find the area under the curve.

P (x<68.5) = 0.2893