Final answer:
The question involves binomial distribution, where a set number of independent trials, each with its own success probability, define a discrete random variable X. The binomial can be approximated by Poisson or normal distribution under specific circumstances.
Step-by-step explanation:
The question is related to the concept of binomial distribution, which is a discrete random variable that results from a set of Bernoulli trials.
In such a distribution, there are a fixed number of independent trials, each with the same probability of success (denoted by p), and the number of successes in these trials is what defines the random variable X.
When the probability of success is low and the number of trials is high, the binomial distribution can be approximated by the Poisson distribution or, under certain conditions, by the normal distribution.
For instance, if an exercise specifies X ~ B(100, .03), it signifies that there are 100 trials with a 3% chance of success in each trial.
The probability of X being less than or equal to a certain number can be calculated using a binomial cumulative distribution function, or approximated with a Poisson distribution if the conditions are met.