Question

A pediatrician has administered a flu vaccine to 1,000 children in a local community. The average number of children who contract the flu after they get vaccinated is 4 cases per 1,000 children. What is the probability that none of the 1,000 children will contract the flu this season? Hint: Use a Poisson distribution with λ = 4. Group of answer choices

Answer 1

Answer:

1.83%

Step-by-step explanation:

For the expected value of 4 cases per 1000 children. We can use a formula for Poisson distribution to calculate the probability that none of the 1000 students would contract the flu:

$P(X = 0) = \frac{\lambda^ke^{-\lambda}}{k!}$

$P(X = 0) = \frac{4^0 e^{-4}}{0!}$

$P(X = 0) = \frac{1}{e^4} = 0.0183$

So the probability of this to happens is 1.83%