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 71 tons of coal into each car.

The actual weights of coal loaded into each car are normally distributed, with mean μ = 71 tons and standard deviation σ = 0.5 ton.

(a) What is the probability that one car chosen at random will have less than 70.5 tons of coal? (Round your answer to four decimal places.)


(b) What is the probability that 24 cars chosen at random will have a mean load weight x of less than 70.5 tons of coal? (Round your answer to four decimal places.)


(c) Suppose the weight of coal in one car was less than 70.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes or No   

Suppose the weight of coal in 24 cars selected at random had an average x of less than 70.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

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

b. Yes, the probability that this deviation is random is very large.    

c. No, the probability that this deviation is random is very small.

d. No, the probability that this deviation is random is very large.

Answer 1

(a)

Let X denote the actual weights of coal loaded into car

Required probability = Probability that one car chosen at random will have less than 70.5 tons of coal = P(X<70.5)

We use Excel function "NORMSDIST()" to find the above value :

Hence,

Probability that one car chosen at random will have less than 70.5 tons of coal = 0.1587

(b)

We need to find :

We use Excel function "NORMSDIST()" to find the above value :

Hence,

Probability that 24 cars chosen at random will have a mean load weight x of less than 70.5 tons of coal = 0

(c)

No, because the probability value is not very low.

(d)

Correct option : a. Yes, the probability that this deviation is random is very small.