What are they asking here? (statistics homework) i am doing some homework in statistics. I have stumbled on a question that i have trouble interpreting what they want. The question is:
Study the probability function for a random variable Y that is bin (100, 0.2). 
Y is approx. N (...... , ......).  
I have made a chart of the binomial distribution using the given function bin (100, 0.2) between 10 and 30. So i can see what the probability for Y is on each of these events. At 10 its 0.0033, at 20 the probability is 0.0993, after that it declines to 0.0051 at 30. 
Do they want me to give like an interval or something? I know N stands for sample size, but I still don't know what data i should supply inside the parenthesis... 
 A: Further along lines of @dieterdvf's Comment:
If $n$ is as large as 100 and Success probability $p$ is not really close
to $0$ or $1,$ then the normal approximation to binomial ought to work
well. 
I'm using vague terms 'as large as' and 'really close' on purpose,
because the fit of normal to binomial is never perfect. (One issue is that
a binomial distribution is not symmetrical unless $p =  1/2,$ whereas the
approximating normal distribution is always symmetrical.) 
Different textbook authors have different "Rules of Thumb" for when it is OK to
use the approximation. You should look in your book to see what rule
is suggested there: Maybe something like, "The smaller of $np$ and $n(1-p)$
should exceed 5."
In your case, you have $X \sim \mathsf{Binom}(n = 100, p=.2),$ for
which $E(X) = np = 20,\,Var(X) = np(1-p) = 16,$ and $SD(X) = 4.$
So you should have $X \stackrel{aprx}{\sim}\mathsf{Norm}(\mu=20,\,\sigma=4).$
But be careful here, in the notation for a normal distribution, some
textbooks use $\sigma$ for variability and others use $\sigma^2.$ So
before you fill in the blanks, you will have to check whether your
question expects 4 or 16 in the blank after the comma.
In the figure below, the vertical bars represent probabilities of
$\mathsf{Binom}(n = 100, p=.2)$ and the curve shows the density function
of $\mathsf{Norm}(\mu = 20, \sigma = 4).$ You can see that the fit
is 'pretty good', but not perfect.

Note: In these days of easy computation with software, it is not really
necessary to rely on normal approximations to get binomial probabilities. 
For example, if you want $P(X \le 12),$ the exact answer to four places is 0.0253, but the
approximate answer from the 'best fitting normal distribution is 0.0304. To two
places, both results are 0.03, which is about the accuracy you can usually expect
from a normal approximation. (Computations below from R statistical software.)
pbinom(12, 100, .2)
## 0.02532875          # exact
pnorm(12.5, 20, 4) 
## 0.03039636

