Here's a question I encountered while practicing for the actuary P/1 exam. I know the answer is 0.88 (because the online quiz where I encountered this told me that was the correct answer), but I need to know how to get the answer:
The chance of an employee being sick during flu season is 20%. What is the probability that less than 4 of 10 employees are sick in a given day?
It sounds like a Poisson distribution to me, with $P(x < 4) = P(3) + P(2) + P(1) + P(0)$
However, when I set $Mu = 0.2$, I got the answer as $0.82$, but when I met $Mu = 2 $( because $10 * 0.2 = 2)$ I got the answer as $0.86$.
Some guidance on where I'm going wrong would be appreciated.
Let $X$ be the number of sick people in a given day, assuming that they are independent of each other, you have that $X\sim Bin(10, 0.2)$, hence $$ P(X < 4) = \sum_{x=0}^3 P(X=x)=\sum_{x=0}^3\binom{10}{x}0.2^x0.8^{10-x}. $$