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 21-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.

(c) Approximate the number of asthma incidents exceeded with probability 5%.

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

Step 1 of 5:

Given the study region in central phoenix, Arizona recorded 10,500 asthma incidents in children in a 21-month period.

Let x = number of asthma incidents per month.

Where x has poisson distribution with mean

Then,

incidents per month.

Z = approximate standard normal random variable.

Step 2 of 5:

a). To find the probability of more than 550 asthma incidents in a month.

= 1- 0.9881

= 0.012

Therefore, the probability of more than 550 asthma incidents in a month is 0.012.

Step 3 of 5:

b). To find the probability of 450 to 550 asthma incidents in a month.

= 0.9864 - 0.0136

= 0.9728

Hence, the probability of 450 to 550 asthma incidents in a month is 0.9728.