Answered: The average fullsized frontloading…

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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The average fullsized frontloading Energy Star clothes washer uses 15 gallons of water per load (greenbuildingadvisor.com, December 4, 2015). Assume that the popula tion standard deviation for the number of gallons of water used to wash a load by these machines is 3.0. a. What is the probability that a random sample of 90 loads washed in a fullsized front loading Energy Star clothes washer will provide a sample mean gallons of water used that is within onehalf gallon of the population mean of 15 gallons? b. What is the probability that a random sample of 50 loads washed in a fullsized front loading Energy Star clothes washer will provide a sample mean gallons of water used that is at least threequarters of a gallon greater than the population mean of 15 gallons? C.What is the probability that a random sample of 75 loads washed in a fullsized front loading Energy Star clothes washer will provide a sample mean gallons of water used that is no more than onequarter of a gallon less than the population mean of 15 gallons?

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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