Coal is carried from a mine in West Virginia to a power plant in New York in hop
ID: 3159272 • Letter: C
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 63 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 63 tons and standard deviation = 1.7 ton.
(a) What is the probability that one car chosen at random will have less than 62.5 tons of coal? (Round your answer to four decimal places.)
(b) What is the probability that 44 cars chosen at random will have a mean load weight x of less than 62.5 tons of coal? (Round your answer to four decimal places.)
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 62.5
u = mean = 63
s = standard deviation = 1.7
Thus,
z = (x - u) / s = -0.294117647
Thus, using a table/technology, the left tailed area of this is
P(z < -0.294117647 ) = 0.384334003 [ANSWER]
**************************
b)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 62.5
u = mean = 63
n = sample size = 44
s = standard deviation = 1.7
Thus,
z = (x - u) * sqrt(n) / s = -1.950955759
Thus, using a table/technology, the left tailed area of this is
P(z < -1.950955759 ) = 0.025531154 [ANSWER]