The probability that a candidate is offered a scholarship is 0.2412. A panel interviews 5 candidates per day for a period of 55 days. Find the probability that, on average, at least 1 candidate is offered the scholarship per day out of this period of 55 days.
The answer is 0.235 (3 s.f.) but I don't know how to get there. You definitely can't use Poisson here right? Someone please help! Also, if the question seems weird, it's because it's the last part of a really long question. I've already solved the other parts of the question, 0.2412 being one of the solutions.
I have no idea how they get 0.235.
5 candidates per day, for 55 days, total 275 candidates. Assuming the candidates' results are independent, and you want at least 55 successes out of them (to make the average at least one per day). So the exact probability is
If you use a normal approximation,
, so you are looking at