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.

ii) 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.

i) Find the probability that in a randomly selected 15000 population, there are at least 181

people who received the AstraZeneca Covid-19 vaccine have severe discomfort

symptoms.

Answer 1

ii)

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

$\lambda=$ 15 per 1000 = 3 per 200

So, $\lambda=3$

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

i)

$\lambda=15\cdot 15000/1000=225$

$P(X\le x)\le \frac{(e\lambda)^xe^{-\lambda}}{x^x}$ for $x<\lambda$

$P(x\ge 181)=1-\frac{(225e)^{181}e^{-225}}{181^{181}}=0.0099$