What is the Difference Between Binomial and Normal Distribution?

The main difference between binomial and normal distribution lies in the nature of the data they represent. Binomial distribution is discrete, meaning it has a finite number of events, while normal distribution is continuous, meaning it has an infinite number of events.

Binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials with identical probability of success. It has two possible outcomes: true or false, success or failure. Some properties of binomial distribution include:

• Mean (μ) = np
• Variance (σ^2) = npq
• Standard Deviation (σ) = √(npq)

where n is the number of trials, p is the probability of success, and q is the probability of failure (q = 1-p).

On the other hand, normal distribution describes continuous data with a symmetric distribution, often referred to as a "bell" shape. It is used to describe various continuous data sets, such as heights or weights of a population. Some key properties of normal distribution include:

• Mean (µ)
• Standard Deviation (σ)

While binomial distribution is inherently discrete, if the sample size for binomial distribution is large enough, its shape will be quite similar to that of normal distribution.

Comparative Table: Binomial vs Normal Distribution

The main differences between binomial and normal distributions are as follows:

In summary, the binomial distribution is a discrete distribution representing the number of successes in a fixed number of independent trials with the same probability of success. On the other hand, the normal distribution is a continuous distribution that represents a wide range of continuous variables. The normal distribution can be used to approximate binomial probabilities under certain conditions, such as large sample sizes and meeting the np and nq requirements.