What is the difference between a normal and binomial distribution?

The Normal distribution is an continuous distribution whereas the Binomial is discrete (takes on only two values).

The main difference between a normal distribution and a binomial distribution lies in the type of data they represent and the conditions under which they are applicable.

A normal distribution is a continuous probability distribution that describes the distribution of a continuous random variable. It is characterized by a symmetric bell-shaped curve, with the mean, median, and mode all being equal. The shape of the curve is determined by the mean and standard deviation of the data. Normal distributions are commonly used to model natural phenomena such as heights, weights, and IQ scores.

On the other hand, a binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has only two possible outcomes (success or failure) and the probability of success remains constant across all trials. The binomial distribution is characterized by a probability mass function that calculates the probability of obtaining a specific number of successes in a given number of trials. Binomial distributions are often used in situations involving binary outcomes, such as coin flips, yes/no questions, or success/failure experiments.

In summary, the main differences between normal and binomial distributions are the type of data they represent (continuous vs. discrete) and the nature of the underlying random process (continuous random variable vs. discrete number of successes in fixed trials).