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 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 tons of coal? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) What is the probability that 35 cars chosen at random will have a mean load weight x of less than 55.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 55.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 35 cars selected at random had an average x of less than 55.5 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.

Answer 1

(a)

= 56

= 0.8

To find P(X<55.5):
Z = (55.5 - 56)/0.8 = - 0.625

Table of Area Under Standard Normal Curve gives area = 0.2357

So,

P(X<55.5) = 0.5 -0.2357 = 0.2643

So

Answer is:

0.2643

(b)

= 56

= 0.8

n = 35

SE = /

= 0.8/ = 0.1352

To find P(<55.5):
Z = (55.5 - 56)/0.1352 = - 3.70

Table of Area Under Standard Normal Curve gives area = 0.4999

So,

P(<55.5) = 0.5 -0.4999 = 0.0001

So

Answer is:

0.0001

(c)

(i)

Correct option:

No

(ii)

Correct option:

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