Question

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

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 52 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 52 tons and standard deviation σ = 1.3 ton. (a) What is the probability that one car chosen at random will have less than 51.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 38 cars chosen at random will have a mean load weight x of less than 51.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 51.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 38 cars selected at random had an average x of less than 51.5 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.

Homework Answers

Answer #1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ= 52
std deviation   =σ= 1.300
probability =P(X<51.5)=(Z<(51.5-52)/1.3)=P(Z<-0.38)=0.3520

b)

sample size       =n= 38
std error=σ=σ/√n= 0.21089
probability =P(X<51.5)=(Z<(51.5-52)/0.211)=P(Z<-2.37)=0.0089

c) Suppose the weight of coal in one car was less than 51.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

No

Would that fact make you suspect that the loader had slipped out of adjustment?

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Coal is carried from a mine in West Virginia to a power plant in New York...
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 pull 73 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 73 tons and standard deviation ? = 0.9 ton. (a) What is the probability that one car chosen at random will have less than 72.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 51 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 51 tons and standard deviation σ = 0.5 ton. (a) What is the probability that one car chosen at random will have less than 50.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 89 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 89 tons and standard deviation σ = 1 ton. (a) What is the probability that one car chosen at random will have less than 88.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 μ = 79 tons and standard deviation σ = 0.7 ton. (a) What is the probability that one car chosen at random will have less than 78.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 68 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 68 tons and standard deviation σ = 1.2 ton. (a) What is the probability that one car chosen at random will have less than 67.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 86 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 86 tons and standard deviation σ = 0.8 ton. (a) What is the probability that one car chosen at random will have less than 85.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 66 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 66 tons and standard deviation σ = 0.5 ton. (a) What is the probability that one car chosen at random will have less than 65.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 57 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 57 tons and standard deviation σ = 0.6 ton. (a) What is the probability that one car chosen at random will have less than 56.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 56 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 56 tons and standard deviation σ = 0.8 ton. (a) What is the probability that one car chosen at random will have less than 55.5...
Coal is carried from a mine in West Virginia to a power plant in New York...
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 61 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 61 tons and standard deviation σ = 0.5 ton. (a) What is the probability that one car chosen at random will have less than 60.5...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT