Answered: b) If a sample of 40 batches of grain…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. A batch processor dispenses a mean volume of approximately 0.70 cubic meter of grain with a standard deviation of 0.06 cubic meter. The volumes of batches are normally distributed. A test engineer wishes to check the calibration of the processor. a) How many batches would have to be measured for the engineer to be 90% confident that the mean volume of the sample is between 0.97 and 1.03 times the true population mean? b) If a sample of 40 batches of grain is measured, with what confidence can the claim be made that the sample mean volume is within 1% of the true mean volume of the population, if the true mean volume is approximately 0.80 cubic meter? c) If a sample of 150 batches of grain is measured, the engineer can be 90% confident that the sample mean is within what percentage of the true population mean? Again, assume that the population mean is approximately 0.80 cubic meter.

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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