Environmental agencies around the world regulate dust pollutants on the basis of
ID: 3176834 • Letter: E
Question
Environmental agencies around the world regulate dust pollutants on the basis of mass, not chemistry, and most governments focus on the particles easiest to catch and quantify; those that are 10 micrometers across (the PM-10 fraction). Federal law prohibits PM-10 concentrations in air from exceeding 150 micrograms per cubic meter (mu g/m^3) over any 24-hour period. If the managers of an industrial park know that they are creating PM-10 concentrations that average 120 (mu g/m^3) with a standard deviation of 15 (mu g/m^3) assuming the PM-10 concentrations are normally distributed, find the following probabilities: That a day's PM-10 concentration is below 140 (mu g/m^3). That a day's PM-10 concentration is between 100 and 140 (mu g/m^3). That a day's PM-10 concentration is above the federal acceptable limit of 150 (mu g/m^3).Explanation / Answer
Average of PM-10 concentrations = 120 g/m3 and standerd deviation = 15 g/m3
(a) P ( X< 140; 120; 15) from Z - table
Z = (140 - 120)/15 = 1.33
from Z - table, respective value of probability P ( X< 140; 120; 15) = 0.9085
(b) Here we have to get P(100<=x <= 140; 120; 15)
we have get z - value for 140 in earlier question, the z- value for 100 is Z = (100 - 120)/15 = -1.33
so P(100<=x <= 140; 120; 15) = P ( x < 140; 120; 15) - P(X<100; 120; 5)
= 0.9085 - 0.0915 = 0.817
(c) so Here we have to calculate probability of PM-10 level above the federal acceptable limit of 150 g/m3
P(x > 150; 120; 15) , Here Z - value = (150 -120)/15 = 2 so for Z = 2 , calculate probability value from Z- table for Z = +2.00
so P(x>= 150; 120; 15) = 0.9772
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