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Solved: An article in Atmospheric Chemistry and Physics

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 107E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 107E

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-by-Step Solution:

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.

 

Step 4 of 5

Chapter 4.7, Problem 107E is Solved
Step 5 of 5

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

The full step-by-step solution to problem: 107E from chapter: 4.7 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This full solution covers the following key subjects: Asthma, incidents, approximate, Probability, month. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. The answer to “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?” is broken down into a number of easy to follow steps, and 121 words. Since the solution to 107E from 4.7 chapter was answered, more than 685 students have viewed the full step-by-step answer.

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Solved: An article in Atmospheric Chemistry and Physics

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