Why use normal approximation to binomial

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Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio voluptates consectetur nulla eveniet iure vitae quibusdam? Excepturi aliquam in iure, repellat, fugiat illum voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos a dignissimos. Close Save changes. Help F1 or? Example Section. Solution There is really nothing new here.

Save changes Close. Most school labs have Microsoft Excel, an example of computer software that calculates binomial probabilities. Many students have access to the TI or 84 series calculators, and they easily calculate probabilities for the binomial distribution. If you type in "binomial probability distribution calculation" in an Internet browser, you can find at least one online calculator for the binomial.

Compare the binomial and normal distribution answers. See Discrete Random Variables for help with calculator instructions for the binomial.

In a city, 46 percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of is taken. Using the continuity correction factor, find the probability that at least favor Dawn Morgan for mayor.

Normal Approximation to the Binomial Distribution Historical Note: Normal Approximation to the Binomial Historically, being able to compute binomial probabilities was one of the most important applications of the central limit theorem. For many binomial distributions , we can use a normal distribution to approximate our binomial probabilities.

This can be seen when looking at n coin tosses and letting X be the number of heads. As we increase the number of tosses, we see that the probability histogram bears greater and greater resemblance to a normal distribution. Every normal distribution is completely defined by two real numbers. These numbers are the mean, which measures the center of the distribution, and the standard deviation , which measures the spread of the distribution.

For a given binomial situation we need to be able to determine which normal distribution to use. The selection of the correct normal distribution is determined by the number of trials n in the binomial setting and the constant probability of success p for each of these trials.

The normal approximation for our binomial variable is a mean of np and a standard deviation of np 1 - p 0. For example, suppose that we guessed on each of the questions of a multiple-choice test, where each question had one correct answer out of four choices. Thus this random variable has mean of 0.

A normal distribution with mean 25 and standard deviation of 4. By using some mathematics it can be shown that there are a few conditions that we need to use a normal approximation to the binomial distribution. The number of observations n must be large enough, and the value of p so that both np and n 1 - p are greater than or equal to This is a rule of thumb, which is guided by statistical practice.

The normal approximation can always be used, but if these conditions are not met then the approximation may not be that good of an approximation. Since both of these numbers are greater than 10, the appropriate normal distribution will do a fairly good job of estimating binomial probabilities. Binomial probabilities are calculated by using a very straightforward formula to find the binomial coefficient.

Unfortunately, due to the factorials in the formula, it can be very easy to run into computational difficulties with the binomial formula. The normal approximation allows us to bypass any of these problems by working with a familiar friend, a table of values of a standard normal distribution.