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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Insulin-dependent diabetes (IDD) is a common chronic

Chapter 3, Problem 199SE

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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?

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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

 

  1. 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

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