The number of times that a person contracts a cold in a give year is a Poisson random variable X with λ=5. Suppose that a new wonder drug (based on large quantitites of vitamin C) has just been marketed that reduces the Poisson parameter to lambda=3 for 75% of the population. For the other 25 percent of the population the drug has no appreciable effect on colds. Showing work and explaining, if we sample 5 individuals that have had 2 colds from this population, what is the probability that for two of those individuals the drug was beneficial?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
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The number of times that a person contracts a cold in a give year is a Poisson random variable X with λ=5. Suppose that a new wonder drug (based on large quantitites of vitamin C) has just been marketed that reduces the Poisson parameter to lambda=3 for 75% of the population. For the other 25 percent of the population the drug has no appreciable effect on colds.

Showing work and explaining, if we sample 5 individuals that have had 2 colds from this population, what is the probability that for two of those individuals the drug was beneficial?

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