Originally Posted by

**chutiya** I am preparing for my finals and came across this question:

$\displaystyle \text{Let p be the probability that the vaccine is a success in any patient.}$

$\displaystyle \text{Find the sample size n and p required to be 95 percent assured that when the}$ $\displaystyle \text{vaccine is given to n infected patients, at least 1000 successful vaccinations will result}$

I am quite confused on this one since we have two unknowns. I tried using binomials distribution with $\displaystyle P(X \geq 1000)\;=\;1-P(X=1000)\;=\;0.95$ with n being the number of patients to be vacinated in order to get at least 1000 successes, but i cannot calculate both $\displaystyle n$ and $\displaystyle p$ from the same equation.

is there any other approach to solve this problem? thank you.