An article under review for Air Quality, Atmosphere Health titled "Linking Particulate Matter (PM10) and Childhood Asthma in Central Phoenix" used PM10 (particulate matter 10µm in diameter) air quality data measured hourly for sensors in Phoenix, Arizona. The 24-hour (daily) mean PM10 for a centrally located sensor was 50.9µg/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 100µg/m³?
b) What is the probability of a daily mean of PM10 less than 25µg/m³?
c) What daily mean of PM10 value is exceeded with probability 5%?