Homework SourseCoal is carried from a mine in West Virginia to a power plan
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 62 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 62 tons and standard deviation = 0.8 ton. (a) What is the probability that one car chosen at random will have less than 61.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 29 cars chosen at random will have a mean load weight x of less than 61.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 61.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 29 cars selected at random had an average x of less than 61.5 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.
Solution
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 61.5
u = mean = 62
s = standard deviation = 0.8
Thus,
z = (x - u) / s = -0.625
Thus, using a table/technology, the left tailed area of this is
P(z < -0.625 ) = 0.265985529 [ANSWER]
*************
b)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 61.5
u = mean = 62
n = sample size = 29
s = standard deviation = 0.8
Thus,
z = (x - u) * sqrt(n) / s = -3.365728004
Thus, using a table/technology, the left tailed area of this is
P(z < -3.365728004 ) = 0.00038171 [ANSWER]
*************
c)
Yes, the probability that this deviation is random is very small.
