So, here is the problem, I have 40 green marbles and 60 red marbles. 20 marbles are taken without replacement. Determine the standard deviation of the number of green marbles taken.
I used the formula for the variance in a hypergeometric distribution: $$n\left(\frac{K}{N}\right)\left(\frac{N-K}{N}\right)\left(\frac{N-n}{N-1}\right)$$
and got:
$$20\left(\frac{40}{100}\right)\left(\frac{60}{100}\right)\left(\frac{80}{99}\right)= 3.\bar{87} $$
I took the root of this and got $\sigma \approx 1.97$ but there is no such answer for me to mark, did I make a mistake? If yes where?
Answering options:
a)0.2329
b)8
c)10.69
d)59.878787...
e)7.74