Still more arrows Suppose our archer from Exercise 18 shoots 10 arrows. a) Find the mean and standard deviation of the number of bulls-eyes she may get. b) Whats the probability that i) she never misses? ii) there are no more than 8 bulls-eyes? iii) there are exactly 8 bulls-eyes? iv) she hits the bulls-eye more often than she misses?

Binomial Distributions Binomial Rules In order for an experiment to be binomial, it must satisfy the following rules: 1 There are a fixed number of observations/trials, which is represented by n 2 The n observations are all independent of each other, i.e. one does not affect the other 3 Each observation falls into one of just two categories, either success or failure 4 The probability of a success, p, is the same for each observation Binomial Random variable, X: counts the number of successes in trials (n = number of trials) of a binomial experiment. (So X = number of successes) Properties of X: o X is a discrete random variable o The possible values of X are 0 - n o The binomial random variable X follows a binomial di