Problem 12 A device that monitors the levels of pollutants has sensors that dete

Question

Problem 12 A device that monitors the levels of pollutants has sensors that detect the amount of CO in the air. Placed in a particular location, it is known that the amount of CO is normally distributed with a mean of 6.23 ppm and a variance of 4.36 ppm2. a. What is the probability that the CO level exceeds 8 ppm? b. What is the probability that the CO level is between 5.2ppm and 8.7ppm? c. An alarm is to activate if the CO levels exceed a certain threshold. Specify the threshold (in ppm) such that it is 3.56 standard deviations above the mean.

Explanation / Answer

here from normal distribution z =(X-mean)/std deviation

std deviation =(varaince)1/2=2.088

a) P(X>8)=1-P(X<8)=1-P(Z<(8-6.23)/2.088)=1-P(Z<0.8477)=1-0.8017=0.1983

b) P(5.2<X<8.7)=P(-0.4933<Z<1.1829)=0.8816-0.3109=0.5707

c)threshold =mean +3.56*std deviation =6.23+3.56*2.088=13.66

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