Question

Coal: Automatic Loader 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 75 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed with a mean tons and standard deviation of 1.5 tons.

a. What is the probability that one car chosen at random will have less than 74 tons of coal?

b. What is the probability that 16 cars chosen at random will have a mean load weight

of less than 74 tons?

c. Interpretation Which probability would cause you to think that the loader had slipped out of adjustment, the probability from part (a) or from part (b)?

Answer 1

Given, μ = 75, σ = 1.5

a)

the probability that one car chosen at random will have less than 74 tons of coal

Here n = 1

Z = (X-μ)/(σ/SQRT(n))

P(X < 74) = P(Z < (​74−75)/(1.5/SQRT(1))​) = P(Z < −0.6667) = 0.2525

b)

the probability that 16 cars chosen at random will have a mean load weight of less than 74 tons

Here n = 16

P(X < 74) = P(Z < (​74−75)/(1.5/SQRT(16))​) = P(Z < −2.6667) = 0.0038

c)

Part b probability is less than the part a probability

So, Part b probability would cause you to think that the loader had slipped out of adjustment