There are 5 conditions for a binomial distribution to be an appropriate model for a random variable:
1. There are a fixed number n of observations
2. The n observations are independent of each other.
3. Each observation falls into one of two categories which are arbitrarily called “success” and “failure”.
4. The random variable X counts the number of “success”.
5. The probability of success p is the same for all observations.
For each situation below identify the attributes of the binomial distribution (if applicable) or identify why the following is not a binomial distribution.
Count the number of heads in 5 flips of a fair coin.
n is
Count the number of boys in sets of identical twins.
n is .
Count the number of questions correct in a multiple choice quiz of 20 questions where every question has 5 possible options and you are just guessing for every question.
n is .
Count the number of months until an individual wins the jackpot in the Pick-4 lottery, if he buys one lottery ticket per month, and plays the same 4 numbers each time.
n is .