Required Information Particles are a major component of air pollution in many areas. It is of Interest to study the sizes of contaminating particles. Let X represent the diameter, In micrometers, of a randomly chosen particle. Assume that In a certain area, the probability density function of X Is Inversely proportional to the volume of the particle; that is, assume that z≥1 f(x) = 0 z<1 where c is a constant. The term PM₁o refers to particles 10 μm or less in diameter. What proportion of the contaminating particles are PMo? (Round the final answer to two decimal places.) The term PM2.5 refers to particles 2.5 um or less in diameter. What proportion of the contaminating particles are PM2.5? (Round the final answer to two decimal places.) What proportion of the PM10 particles are PM2.5? (Round the final answer to three decimal places.)
Required Information Particles are a major component of air pollution in many areas. It is of Interest to study the sizes of contaminating particles. Let X represent the diameter, In micrometers, of a randomly chosen particle. Assume that In a certain area, the probability density function of X Is Inversely proportional to the volume of the particle; that is, assume that z≥1 f(x) = 0 z<1 where c is a constant. The term PM₁o refers to particles 10 μm or less in diameter. What proportion of the contaminating particles are PMo? (Round the final answer to two decimal places.) The term PM2.5 refers to particles 2.5 um or less in diameter. What proportion of the contaminating particles are PM2.5? (Round the final answer to two decimal places.) What proportion of the PM10 particles are PM2.5? (Round the final answer to three decimal places.)
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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Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen particle. Assume that in a certain area, the
f(x) = {c/x3 x≥1
0 x<1
where c is a constant.
1. The term PM10 refers to particles 10 μm or less in diameter. What proportion of the contaminating particles are PM10? (Round the final answer to two decimal places.)
2. The term PM2.5 refers to particles 2.5 μm or less in diameter. What proportion of the contaminating particles are PM2.5? (Round the final answer to two decimal places.)
3. What proportion of the PM10 particles are PM2.5? (Round the final answer to three decimal places.)
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Required information
Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles.
Let X represent the diameter, In micrometers, of a randomly chosen particle. Assume that In a certain area, the probability
density function of X Is Inversely proportional to the volume of the particle; that is, assume that
z > 1
f(x) =
0
z <1
where c is a constant.
The term PM₁0 refers to particles 10 pm or less in diameter. What proportion of the contaminating particles are PM₁o? (Round the final answer to two decimal places.)
The term PM2.5 refers to particles 2.5 µm or less in diameter. What proportion of the contaminating particles are PM2.5? (Round the final answer to two decimal places.)
What proportion of the PM10 particles are PM2.5? (Round the final answer to three decimal places.)
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VIEWStep 2: Find the value of c and the rewrite the function.
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VIEWStep 4: Find the proportion of the contaminating particles are PM2.5
VIEWStep 5: Find the proportion of PM10 particles are PM2.5
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