1 1. If X has a binomial distribution, X is counting the number of 'successes' found in the sample of size n. We know the variance is np(1-p). TAT 1430 Recitation Normal and Binomial Review a. Choose a value of n, and graph the variance function f(p) = np(1-p) where the values of p go from 0 to 1. It should look like a parabola opening downwards. (Hint, you can rewrite it as f(x) = nx(1-x) and let x go from 0 to 1.) b. For which value(s) of p is the variance of X the largest? (Don't change n.) c. Why does this make sense? d. For which value(s) of p is the variance of X the smallest? (Don't change n.) e. Why does this make sense