A device that monitors the levels of pollutants has sensors that detect the amou

Question

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

z = (X-Mean)/SD
Standard deviation = sqrt Variance = sqrt 4.36

a) z = (8.0 - 6.23) / sqrt 4.36 = + 0.847 approximately
The area under the standard normal curve right to the z value indicates the required probability.
Required probability = P(X > 8.0)
= P(z > 0.847)
= 0.2005

b) z1 = (5.2 - 6.23)/sqrt 4.36 = - 1.826
z2 = (8.7 - 6.23) / sqrt 4.36 =1.182
The area under the standard normal curve between these two z values indicates the required probability.
Required probability = P(5.2 < X < 6.23)
= P(- 1.826 < z < 1.182)
= P(z < 1.182) - P(z < - 1.826)
= 0.8810- 0.344

= 0.537

c) Required threshold level = Mean + 3.56*SD
= 6.23 + 3.56*4.36
= 24.75 ppm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.