Answer the following: A) Find he binomal probability of p(x=5) where n=13 and p=0.50 B) Set up, without solving, the binomial probability p(x is at most 5) using probability notation. C) How would you find the formula for the normal approximation to the binomial, and show the final formula ou would ue without going through all the calculations. Solution Given X~Binomial(n=13, p=0.5) P(X=x) = xC13*(0.5^13) (a) P(X=5) = 5C13*(0.5^13) =1287*(0.5^13) =0.1571 --------------------------------------------------------------- (b) P(X<=5) = P(X=0)+...+P(X=5) ---------------------------------------------------------------- (c) By using Normal approximation, X~Normal(mean=n*p, s^2=n*p*(1-p)).

1. Answer the following:
A) Find he binomal probability of p(x=5) where n=13 and p=0.50
B) Set up, without solving, the binomial probability p(x is at most 5) using probability notation.
C) How would you find the formula for the normal approximation to the binomial, and show the
final formula ou would ue without going through all the calculations.
Solution
Given X~Binomial(n=13, p=0.5) P(X=x) = xC13*(0.5^13) (a) P(X=5) =
5C13*(0.5^13) =1287*(0.5^13) =0.1571 ---------------------------------------------------------------
(b) P(X<=5) = P(X=0)+...+P(X=5) ---------------------------------------------------------------- (c) By
using Normal approximation, X~Normal(mean=n*p, s^2=n*p*(1-p))