Question 1110343: 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 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 73 tons and standard deviation σ = 0.8 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.)
.2676
Incorrect: Your answer is incorrect.
(b) What is the probability that 36 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.)
-273.8184 < my answer
Incorrect: Your answer is incorrect.
(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 36 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.
I need help with the probability intervals. Im not sure what i did wrong. Can anyone help?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z<(72.5-73)/0.8 or z<-0.625. General form for z is (x-mean)/s.d.
probability is 0.2660. Yours should be close enough, since you used -0.62. Apparently, they did not want z rounded at all.
For 36 cars, z < (x bar-mean)/0.8/sqrt(36)
This is -0.5*6/0.8=-3/.8=-3.75. That probability is 0.000088
One car's being below 72.5 would occur one time out of four. It should not be a cause for alarm in this instance.
Probability can never be negative or greater than 1. The last ne is the probability that this deviation is random is very small. It is extraordinarily small.
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