Question: An article in Atmospheric Chemistry and Physics ['Relationship Between Particulate Matter and Childhood Asthma - Basis of a Future Warning System for Central Phoenix: 2012,

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) linked air quality to childhood asthma incidents. The study region in central Phoenix, Arizona recorded 10,500 asthma incidents in children in a a-month period. Assume that the number of asthma incidents follows a Poisson distribution.

(a) Approximate the probability of more than 550 asthma incidents in a month.

(b) Approximate the probability of 450 to 550 asthma incidents in a month.

(d) If the number of asthma incidents was greater during the winter than the summer, what would this imply about the Poisson distribution assumption?

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