What the heck is a binomial setting?!

        *It has a fixed number of independent trials!
        *It has a fixed probability of success!
        *Observations can be classified as either success or failure!
        *AND...if n is large we can just assume it's binomial!!!

Let's do some notation!

    *B(n,p) is a binomial distribution for the count X of successes where n is the number of observations and p is the probability of a success on any single observation!

Get your calculator out!

    *To get individual probabilities!:

        binompdf(n,p,X) can help us find stuff like P(X=1) or P(X=2)!  Yeah!

              So let's do some stats!

                            Roll a die 20 times and count the number of 3's!  Find P(X=7)!
                                            binompdf (20, 1/6, 7) = .0259!!!!!

    *To get cumulative probabilities!:
        binomcdf(n,p,X) gives us the sum of probabilities up to X!  (YES THIS INCLUDES X!!)  We can find stuff like P(X<1) or
        P(X<2)!

              Fish on?!

                        Roll a die 20 times and count the number of 3's!  Find P(X<4)!
                                        binomcdf(20, 1/6, 4) = .7687!
                        Now find P(X>4)!
                                        1-P(X<4) = 1-binomcdf(20, 1/6, 4) = 1-.7687 = .2313!

What if the calculator breaks?!

        Binomial Formula for k successes!:
                P(X=k) =   n!    {p^k (1-p)^(n-k)}
                             k!(n-k)!

      Other formulas!:

               *mean = np
                *variance = np(1-p)
                *standard deviation = 

It looks pretty normal to me...!

                Conditions for approximating binomial functions as normal!:

                    *n must be large and the conditions np>10 and n(1-p)>10 must be met!
                    *Then we can say X is approx. N(np, ) and use normalcdf(min, max, mean, st. dev.)!