Question

g Nationwide, a certain disease occurs only a small proportion of people (.000215). A certain town has 74,000 residents. Use the Poisson approximation. c) Determine the probability that the town has 30 or fewer residents with the illness.

Answer 1

The probability that the town has 30 or fewer residents with the illness = 0.00052.

Explanation:

So, we have the following set of data or information or parameters given from the question above and they are; the number of people living in that particular society/community/town = 74,000 residents and the proportion of people that the diseases affected = .000215.

The first step to do is to determine the expected number of people with disease. Thus, the expected number of people with disease = 74,000 × .000215 = 15.91.

Hence, the probability that the town has 30 or fewer residents with the illness = 1.23 × 10^-7 × 15.91^30/ 2.65253 × 10^-32 = 0.00052.

Note the formula used in the calculating the probability that the town has 30 or fewer residents with the illness = e^-λ × λ^x/ x!