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An article in Atmospheric Chemistry and Physics
Chapter 4, Problem 89E(choose chapter or problem)
Problem 89E
An article in Atmospheric Chemistry and Physics “Relationship Between Particulate Matter and Childhood Asthma— Basis of a Future Warning System for Central Phoenix” (2012, Vol. 12, pp. 2479–2490)] reported the use of PM10 (particulate matter ◊◊10 ◊m diameter) air quality data measured hourly from sensors in Phoenix, Arizona. The 24-hour (daily) mean PM10 for a centrally located sensor was 50.9 ◊g/m3 with a standard deviation of 25.0. Assume that the daily mean of PM10 is normally distributed.
(a) What is the probability of a daily mean of PM10 greater than 100 ◊g/m3?
(b) What is the probability of a daily mean of PM10 less than 25 ◊g/m3?
(c) What daily mean of PM10 value is exceeded with probability 5%?
Questions & Answers
QUESTION:
Problem 89E
An article in Atmospheric Chemistry and Physics “Relationship Between Particulate Matter and Childhood Asthma— Basis of a Future Warning System for Central Phoenix” (2012, Vol. 12, pp. 2479–2490)] reported the use of PM10 (particulate matter ◊◊10 ◊m diameter) air quality data measured hourly from sensors in Phoenix, Arizona. The 24-hour (daily) mean PM10 for a centrally located sensor was 50.9 ◊g/m3 with a standard deviation of 25.0. Assume that the daily mean of PM10 is normally distributed.
(a) What is the probability of a daily mean of PM10 greater than 100 ◊g/m3?
(b) What is the probability of a daily mean of PM10 less than 25 ◊g/m3?
(c) What daily mean of PM10 value is exceeded with probability 5%?
ANSWER:
Solution :
Step 1 of 3:
Given that mean PM10 for a centrally located sensor is 50.9 with a standard deviation of 25.
We assume that the daily mean of PM10 is normally distributed.
Let X denote the daily mean of PM10.
a). We need to find the probability of a daily mean of PM10 greater than 100 .
We know that and .
P(X>100) = P
P(X>100) = P
P(X>100) = 1-P(Z>1.964)
Using areas under the normal probability table,
P(X>100) = 1-0.9750
P(X>100) = 0.025
Therefore, the probability of a daily mean of PM10 greater than 100 is 0.025.