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The number of times that a person contracts a cold in a
Chapter 4, Problem 60P(choose chapter or problem)
Problem 60P
The number of times that a person contracts a cold in a given year is a Poisson random variable with parameter λ = 5. Suppose that a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to λ = 3 for 75 percent of the population. For the other 25 percent of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has 2 colds in that time, how likely is it that the drug is beneficial for him or her?
Questions & Answers
QUESTION:
Problem 60P
The number of times that a person contracts a cold in a given year is a Poisson random variable with parameter λ = 5. Suppose that a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to λ = 3 for 75 percent of the population. For the other 25 percent of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has 2 colds in that time, how likely is it that the drug is beneficial for him or her?
ANSWER:
Solution:
Step 1 of 2:
Let X = number of times individual catches a cold in a year.
B = event that drug is beneficial.
Let X follows the Poisson distribution with the probability mass function
P(X = x) =
We have the parameter = 3 for 75 percent of the population and remaining 25 percent of the population the drug has no appreciable effect on colds.
If an individual tried the drug for a year and has 2 colds in that time, then the claim is to check how likely is that drug is beneficial for him or her.