Question

The binomial distribution and the normal distribution are similar in a number of ways, although they are different distributions. Distinguish the basic differences between the two distributions. Give an example of binomial and normal experiments.

Answer 1

The binomial distribution and the normal distribution have several key differences. The binomial distribution is discrete, while the normal distribution is continuous. The binomial distribution deals with a fixed number of trials, while the normal distribution can represent any value within a given range. The binomial distribution is characterized by the number of trials and the probability of success, while the normal distribution is characterized by the mean and standard deviation.

Step-by-step explanation:

The basic differences between the binomial distribution and the normal distribution are as follows:

1. Shape: The binomial distribution is a discrete distribution with a fixed number of possible outcomes, while the normal distribution is a continuous distribution with an infinite number of possible outcomes. The binomial distribution has a histogram that appears as a series of bars, while the normal distribution has a symmetrical bell-shaped curve.
2. Variables: The binomial distribution deals with a random variable that represents the number of successes in a fixed number of trials, while the normal distribution deals with a random variable that can represent any value within a given range.
3. Parameters: The binomial distribution is characterized by the parameters n and p, which represent the number of trials and the probability of success respectively, while the normal distribution is characterized by the parameters μ and σ, which represent the mean and standard deviation respectively.

An example of a binomial experiment is flipping a fair coin 10 times and counting the number of heads. An example of a normal experiment is measuring the heights of a large group of people.