Question

Which of the following is not a requirement to model with the binomial distribution?

a. A discrete random variable
b. A constant probability of success
c. Between exactly two possible states for the random variable
d. Less than 25 trials

Answer 1

The correct answer is d. The incorrect requirement for the binomial distribution is 'Less than 25 trials' as binomial experiments can include any fixed number of trials regardless of the quantity.

Step-by-step explanation:

The question involves identifying the inaccurate requirement for modeling with the binomial distribution. The correct requirements for a binomial experiment are:

1. A discrete random variable.
2. A constant probability of success throughout the trials.
3. Only two possible outcomes for the random variable, commonly referred to as 'success' and 'failure'.
4. A fixed number of independent trials.

The option that is not a requirement for the binomial distribution is 'd. Less than 25 trials'. This statement is incorrect because the number of trials in a binomial experiment can be any positive integer – there is no upper limit of 25 trials for a binomial distribution. Therefore, the correct answer to the student's question is option d.