Basic Statistics05 marksNumerical: Poisson distribution probabilityPoisson distribution
The rate of denying to take vaccine for COVID19 in a rural population of India is reported to be 0.45 per 10,000 people. If the distribution of denying follows Poisson distribution, what is the probability that in the next 10,000 people, there will be: a.)No one will deny to take vaccine? b.)At leas
The rate of denying to take vaccine for COVID19 in a rural population of India is reported to be 0.45 per 10,000 people. If the distribution of denying follows Poisson distribution, what is the probability that in the next 10,000 people, there will be: a.)No one will deny to take vaccine? b.)At least two persons will deny to take vaccine? [5]
- Rate of vaccine denial = 0.45 per 10,000 people - Distribution: Poisson - Sample size for prediction = 10,000 people - Therefore, $\lambda = 0.45$ $$P(X = k) = \frac{e^{-\lambda}\lambda^k}{k!}$$ $$P(X=0) = \frac{e^{-0.45}(0.45)^0}{0!} = e^{-0.45}$$ Computing $e^{-0.45}$: $$e^{-0.45} = 0.63763$$...