Answered: An air filter has been designed to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

An air filter has been designed to remove particles. One test requires 40 air samples to be analyzed. Out of 40 samples, it was found that there were no particles in 15 samples, one particle in 10 samples, two particles in 8 samples, three particles in 5 samples, and four particles in 2 samples.

a) What type of distribution should the data follow? What are the necessary assumptions?

b) Estimate the mean and standard deviation of the frequency distribution from the given data.

c) What is the theoretical standard deviation of the probability distribution?

d) Using probabilities calculated from the theoretical distribution, what is the probability that among ten specimens there are eight or more without particles?

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 + ...

Expert Solution