The Central Limit Theorem

The Central Limit Theorem is very useful when the distribution is unknown for making calculations with the mean and other statistics. However, in the case of calculating the percentage of a population with a non-normal distribution, the percentage included in an interval is not appropriate.

Uniform Distribution

In this work, we start from a known distribution, the uniform distribution. Recall that the uniform distribution U(a, b) has a mean of (a+b)/2 and a variance of (b-a)^2/12.

Parameters for Normal Distribution

The mean and variance of the uniform distribution will be used as the parameters that define a normal distribution.

Application Details

The application available at https://diyeipetea.shinyapps.io/CourseProject3/ allows you to select the minimum and maximum values that define a uniform distribution. You can also choose the probability for a probability interval centered on the mean, which will serve to check the risk of using the normal distribution as an approximation to a non-normal distribution (uniform in this case). You also need to choose the size of the random samples. With these parameters, the application indicates the interval centered on the mean, the percentage of data from the sample with a uniform distribution included in that interval, and the percentage of data from the sample with the approximated normal distribution that are in that interval. I hope you find this experiment interesting. Thank you very much.

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