Question

In your own words, and in a non-technical manner without using any equations, explain the relationship between the binomial distribution and the normal distribution. (You may use phrases like "large n", mean , SD etc.)

Answer 1

The binomial distribution and the normal distribution are related through the central limit theorem. The binomial distribution models the number of successes in a fixed number of trials, while the normal distribution is used to approximate the binomial distribution when the number of trials is large.

Step-by-step explanation:

The binomial distribution and the normal distribution are related through the central limit theorem. The binomial distribution is used to model the number of successes in a fixed number of independent trials, while the normal distribution is used to approximate the binomial distribution when the number of trials is large. In other words, as the sample size (n) increases, the sampling distribution of the mean, which is based on the binomial distribution, approaches a normal distribution.

For example, let's say we have a binomial experiment where we flip a fair coin 100 times. The binomial distribution would tell us the probability of getting a certain number of heads. However, if we increase the number of flips to, let's say, 1000, the binomial distribution would become very difficult to compute. Instead, we can use the normal distribution to approximate the binomial distribution by taking into account the mean and standard deviation of the binomial distribution.