Suppose that 40% of American homes have a microwave oven. Let X be the number of American homes in a random sample of n=25 that have a microwave oven. Find the probability that X is at most 11 and at least 8.


Helping someone review Prob & Stats before their final.
It's been a while since I messed with this, and I can't remember which distribution to use. Any help?

I think I tried to over-complicate this. I ended up choosing Binomial Distribution
p=.4
q=.6
n=25

Obviously a discrete function, so:
P[8<=X<=11] = f(8) + f(9) + f(10) + f(11)


Please let me know if I chose the wrong distribution!

Binomial is obviously the good choice... as long as the "random" sample is random (not gonna happen in real life).

Yes, P(X is in [8;11]) = p (X=8) + ... + p (X=11)
= ( 8 25 ) * 0.4 ^8 * 0.6 ^ 17 + ( 9 25 ) * 0.4 ^ 9 * 0.6 ^ 16 + ... + ( 11 25 ) * 0.4 ^ 11 * 0.6 ^ 14

Terrific, thanks. Would've felt bad if I gave the wrong advice

http://en.wikipedia.org/wiki/Chebyshev's_inequality

???