Q: Derive normal distribution as a limiting case of binomial distribution?

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There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.

Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.

The binomial distribution can be approximated with a normal distribution when np > 5 and np(1-p) > 5 where p is the proportion (probability) of success of an event and n is the total number of independent trials.

The binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of draws from a finite population, with replacement. The hypergeometric distribution is similar except that it deals with draws without replacement. For sufficiently large populations the Normal distribution is a good approximation for both.

As n increases, the distribution becomes more normal per the central limit theorem.

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The de Moivre-Laplace theorem. Please see the link.

Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.

There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.

Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.

It is necessary to use a continuity correction when using a normal distribution to approximate a binomial distribution because the normal distribution contains real observations, while the binomial distribution contains integer observations.

The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

The binomial distribution can be approximated with a normal distribution when np > 5 and np(1-p) > 5 where p is the proportion (probability) of success of an event and n is the total number of independent trials.

No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

You can use a normal distribution to approximate a binomial distribution if conditions are met such as n*p and n*q is > or = to 5 & n >30.

Normal Distribution is a key to Statistics. It is a limiting case of Binomial and Poisson distribution also. Central limit theorem converts random variable to normal random variable. Also central limit theorem tells us whether data items from a sample space lies in an interval at 1%, 5%, 10% siginificane level.

A small partial list includes: -normal (or Gaussian) distribution -binomial distribution -Cauchy distribution

The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.