There are twelve green and eight yellow balls in a bag. One ball is drawn from the bag at random and
replaced. This is repeated until a yellow ball is drawn. The number of balls drawn in total is X.
(a) Find the mean and variance of X.
(b) Find the probability that X is at most one standard deviation from E(X)
I have found the mean as 5/2 and the variance as 15/4.
I’m not sure how to do part b. I know that with a normal distribution it would be 68 percent but I’m not sure how to do it with a negative binomial. Any help would appreciated. Thanks