**Understanding Poisson Distribution: A Practical Application**An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2000 individuals, we want to determine the approximate distribution of the number who carry this gene. This can be approximated using the Poisson distribution with a mean (μ) value that needs to be calculated.**Problem Statement:**We can approximate this distribution by the Poisson distribution with μ = [ ].1. **Part (a):** Using the Poisson approximation, calculate the approximate probability that between 3 and 7 individuals (inclusive) carry the gene. (Round your answer to three decimal places.) - Input box for answer: [ ]2. **Part (b):** Use the Poisson approximation to calculate the approximate probability that at least 7 individuals carry the gene. (Round your answer to three decimal places.) - Input box for answer: [ ]To solve these problems, you may need to refer to the appropriate table in the Appendix of Tables.**Additional Resources:**- **Need Help?** - **Read It**: Provides access to textual resources for understanding the Poisson distribution. - **Watch It**: Offers video explanations and tutorials on applying the Poisson approximation.This exercise illustrates how the Poisson distribution is used to model rare events over a fixed interval, making it a valuable tool in genetic research and other fields.

(a) Use the Poisson approximation to calculate the approximate probability that between 3 and 7 (inclusive) carry the gene. (Round your answer to three decimal places.) (b) Use the Poisson approximation to calculate the approximate probability that at least 7 carry the gene. (Round your answer to three decimal places.)

(a) Use the Poisson approximation to calculate the approximate probability that between 3 and 7 (inclusive) carry the gene. (Round your answer to three decimal places.) (b) Use the Poisson approximation to calculate the approximate probability that at least 7 carry the gene. (Round your answer to three decimal places.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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