We are given a list of males and females in Column A. Adding them all up there are 93. Of which 53 are males and 40 females. The probabilities are (.57,.43). I am asked to find the probability exactly 6 males:
$n=93$
$s=6$
$p(s)=.57$
Using excel I get the value $3.38142E=-25$
That seems like such a small number, I feel like there is something wrong with calculations? Should I be using the number of trials of only males, but that doesn't seem right? For anyone that knows excel I used binom.dist(6,93,.57,"FALSE")
This is not surprising at all. Your binomial distribution has mean $\mu = .57*93 \approx 50$ and standard deviation $\sigma = \sqrt{93*.57*.43} \approx \sqrt{25} \approx 5$. Obtaining $6$ is a deviation of $-44$, nine times the standard deviation, which is an incredibly rare event. You discovered the power of the law of large numbers. Once you have a population in the tenths of people, it is very unlikely to deviate from the mean by a lot.