**Understanding the Poisson Distribution in Genetic Research**An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 1500 individuals, the goal is to approximate the distribution of the number of people who carry this gene.**Poisson Distribution Approximation**The Poisson distribution can be used to approximate this situation with a mean (\(\mu\)) of 3.**Questions:**(a) **Probability Calculation:** Use the Poisson approximation to calculate the probability that between 4 and 9 (inclusive) individuals carry the gene. Ensure that your answer is rounded to three decimal places. - Input: [ ](b) **Probability Calculation:** Use the Poisson approximation to calculate the probability that at least 9 individuals carry the gene. Ensure that your answer is rounded to three decimal places. - Input: [ ]*Note: You may need to use the appropriate table in the Appendix of Tables to answer this question.*

Formula : poisson distribution is given by

Answered: An article reports that 1 in 500 people…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
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An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2500 individuals, what is the approximate distribution of the number who carry this gene? We can approximate this distribution by the Poisson distribution with μ = 5 (a) Use the Poisson approximation to calculate the approximate probability that between 6 and 11 (inclusive) carry the gene. (Round your answer to three decimal places.) 0.214 X (b) Use the Poisson approximation to calculate the approximate probability that at least 11 carry the gene. (Round your answer to three decimal places.) 0.0028 x You may need to use the appropriate table in the Appendix of Tables to answer this question.
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In 1898, L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.61. (a) What is the probability of more than 1 death in a corps in a year? (b) What is the probability of no deaths in a corps over 6 years? Round your answers to four decimal places (e.g. 98.7654). (a) The probability is i ! (b) The probability is i
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