Question

1. How do you know when to use the binomial distribution to model a situation? What are the requirements for a binomial experiment? [4 bullets] 2. When dealing with the binomial distribution, why are the possible values for the random variable always 0,1,2,3,…,n where n is the number of trials or sample size? Why can't we use negative values, or fractions, or numbers greater than n ? [3 sentences] 3. Under what conditions is a binomial distribution symmetric? Skewed left? Skewed right? Why? [3 sentences] 4. How is the area in the bars of a binomial histogram related to the probability of choosing those X values? (Hint: figure it out for a single bar) [3 sentences]

Answer 1

The binomial distribution is suitable when there are a fixed number of independent trials with two possible outcomes, and the probability of success remains constant. The possible values in a binomial distribution are limited to 0, 1, 2, 3, …, n (the number of trials), excluding negative values, fractions, or values greater than n.
The binomial distribution is symmetric when the probability of success equals the probability of failure, while it is skewed left when the probability of success is greater than 0.5, and skewed right when the probability of success is less than 0.5.