An article in Atmospheric Chemistry and Physics

Chapter 4, Problem 89E

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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%?

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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.


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