Coal is carried from a mine in West Virginia to a power plant in New York in hop

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 79 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 79 tons and standard deviation = 1 ton.

(a) What is the probability that one car chosen at random will have less than 78.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 41 cars chosen at random will have a mean load weight x of less than 78.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 78.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

YesNo     

Suppose the weight of coal in 41 cars selected at random had an average x of less than 78.5 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.

Explanation / Answer

mean = 79
std. dev. = 1

a)
P(X < 78.5)
= P(z < (78.5 - 79)/1))
= P(z < -0.5)
= 0.308537539

b)
P(X < 78.5)
= P(z < (78.5 - 79)/(1/sqrt(41)))
= P(z < -3.2015)
= 0.000683

c)
No, because probability of missing one truck is higher.

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

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