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Insulin-dependent diabetes (IDD) is a common chronic
Chapter 3, Problem 199SE(choose chapter or problem)
Problem 199SE
Insulin-dependent diabetes (IDD) is a common chronic disorder in children. The disease occurs most frequently in children of northern European descent, but the incidence ranges from a low of 1–2 cases per 100,000 per year to a high of more than 40 cases per 100,000 in parts of Finland.4 Let us assume that a region in Europe has an incidence of 30 cases per 100,000 per year and that we randomly select 1000 children from this region.
a Can the distribution of the number of cases of IDD among those in the sample be approximated by a Poisson distribution? If so, what is the mean of the approximating Poisson distribution?
b What is the probability that we will observe at least two cases of IDD among the 1000 children in the sample?
Questions & Answers
QUESTION:
Problem 199SE
Insulin-dependent diabetes (IDD) is a common chronic disorder in children. The disease occurs most frequently in children of northern European descent, but the incidence ranges from a low of 1–2 cases per 100,000 per year to a high of more than 40 cases per 100,000 in parts of Finland.4 Let us assume that a region in Europe has an incidence of 30 cases per 100,000 per year and that we randomly select 1000 children from this region.
a Can the distribution of the number of cases of IDD among those in the sample be approximated by a Poisson distribution? If so, what is the mean of the approximating Poisson distribution?
b What is the probability that we will observe at least two cases of IDD among the 1000 children in the sample?
ANSWER:
Solution:
Step 1 of 2:
IDD is a Insulin dependent diabetes is a common chronic disorder in children.
The disease occurs most frequently in children of northern European descent.
A region in Europe has an incidence of 30 cases per 100,000 per year and that we randomly select 1000 children from this region
- The claim is to to suggest the sample is approximated by a Poisson distribution and if so, we have to find the mean of the approximated Poisson distribution
The sample is approximated by a Poisson distribution, because an average rate has been given.
The mean of the Poisson distribution is =
= 1000
= 0.3
Hence, the mean of the poisson distribution is 0.3