Question

In: Statistics and Probability

12 cases of a disease are found over an area of 50 square miles. (what type...

12 cases of a disease are found over an area of 50 square miles.

(what type of distribution is this, i.e. Poisson, Gaussian, etc.)

  1. Within the study area, if the cases are distributed at random places with the same chance to occur anywhere, what is the probability of finding 4 cases within an 8 square mile area? Calculate by hand.
  2. What is the average number of cases within the 8 square mile area? Calculate by hand.

Solutions

Expert Solution

We use Poisson distribution for calculating the probability of events that occur in some specified interval of time or space when the average rate of occurrence is constant.

It was given that 12 cases of a disease are found over an area of 50 square miles. (a constant average rate of occurrence)

Therefore the number of cases of that disease in some square mile area follows a Poisson distribution

Let X be the number of cases of a disease found within an 8 square mile area

12 cases of a disease are found over an area of 50 square miles.

==> 1.92 cases of a disease are found per 8 square miles (constant average rate, )

where x = 0,1,2,..... and = 1.92

Therefore the probability of finding 4 cases within an 8 square mile area is 0.083

The average number of cases within the 8 square mile area = = 1.92

orchestra answered 2 years ago
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