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 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 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 45 cars chosen at random will have a mean load weight x of less than 56.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 56.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

  

Suppose the weight of coal in 45 cars selected at random had an average x of less than 56.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Choices:

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.

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	57
std deviation   =σ=	0.6000

probability that one car chosen at random will have less than 56.5 tons of coal

probability =

P(X<56.5)

=

P(Z<-0.83)=

0.2033

b)

sample size       =n=	45
std error=σx̅=σ/√n=	0.0894

probability =

P(X<56.5)

=

P(Z<-5.59)=

0.0000

c)

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