Supposing that historical data show that 10% of a given population show an allergic reaction to a particular drug, and 60 persons are randomly selected to take part on a study for allergic reactions, a binomial experiment can be used to determine 1) whether or not 6 or them experience allergic reactions, or 2) whether or not more than 6 of them exhibit allergic reactions. In this example n = 60, p = 0. 10, and x = 6.
Explain why this application can be modeled using the binomial distribution. The aforementioned experiment can be modeled after the binomial distribution because it exhibits the following characteristics: 1) It consists of a fixed number (n) of trials, 2) there are only two possible outcomes for each scenario, 3) the probabilities are the same for each trial, and 4) all trials are independent (meaning, each trials outcome does not have an effect on other trials).