Provide a statistical for the following.

1.Why Researchers might make approximations using normal distribution when the real distribution is a bit different from the perfect normal distribution

The obvious reason normal distribution is often used is that it requires the least computations due to its straightforwardness compared to other distributions. This is why most researchers resolve to use it even when the real distribution of the data at hand is a bit different from the perfect normal distribution.

Another reason why researchers make approximations using normal distribution is described by Yakir (2011) that computations based on the Normal approximation "will be valid for all members in the class of distributions, including cases where we don't have the computational tools at our disposal or even in cases where we do not know what the exact distribution of the member is!" (p. 97).

Lumen Learning (n.d.) note that researchers also use approximations using the normal distribution because "the scope of the normal approximation follows with the statistical themes of the law of large numbers and central limit theorem" (para. 6). Thus, the Normal distribution portrays real-world situations with a few exceptions that require other distributions such as the Uniform and Exponential distributions.

2 In statistics, the reason for approximation is when the answer is not exact, but it is similar, this often might lead to a complex calculation.

Researchers may use approximations as a means of assuming the outcome in a probability. Especially if the value is often present and occurs naturally, this can lead to the initial approximation.

According to Yakir (2011)," researchers use normal distribution approximation where there no computational tool to handle a particular data set or where the exact distribution is unknown because the computation of normal distribution will be valid for all members in the class of distributions" (p. 97).

If the researchers are conversant with the normal distribution, this helps them analyze the experiment, studies, or probability of set data they work with.

3 Calculating data using binomial and Poisson will give you exact computation of the data but with normal distribution you have an approximation value which is usually three decimal points correct to the actual computation. In some cases, sizes in number of events and probability can result in inaccuracy of normal distribution when compared to actual computation of binomials and Poisson so researchers make approximations to have a relatively close value to the actual computation.