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 μm 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 μg/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 μg/m³?

(b) What is the probability of a daily mean of PM10 less than 25 μg/m³?

(c) What daily mean of PM10 value is exceeded with probability 5%?