Answer to Question #248892 in Statistics and Probability for Kiirthi

Question

The number of AstraZeneca Covid-19 vaccine recipients who had severe discomfort symptoms

found to be 15 per 1000 population. Assuming the number of people who received the

AstraZeneca Covid-19 vaccine had severe discomfort symptoms follows a Poisson distribution.

Find the probability that in a randomly selected 200 population, there are 4 or 5 people

who received the AstraZeneca Covid-19 vaccine have severe discomfort symptoms.

Answer 1

$P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}$

$\lambda=$ 15 per 1000 = 3 per 200

So, $\lambda=3$

$P(4\ or\ 5)=P(4)+P(5)=\frac{3^4e^{-3}}{4!}+\frac{3^5e^{-3}}{5!}=0.1680+0.1008=0.2688$