Answered: Coal is carried from a mine in West…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 66 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 66 tons and standard deviation ? = 1.3 ton.

(a) What is the probability that one car chosen at random will have less than 65.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 31 cars chosen at random will have a mean load weight x of less than 65.5 tons of coal? (Round your answer to four decimal places.)

(c) Suppose the weight of coal in one car was less than 65.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes or No ? No

Suppose the weight of coal in 31 cars selected at random had an average x of less than 65.5 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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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