Reproducible Pitch Presentation

Normal distributions are useful because:

• They are common
• Their properties are known

As a result, we can use the knowledge about Normal distibutions to solve practical problems. For example, if we know that a certain characteristic of a population of interest is normally distributed and we knbow the parameters of the distribution, we can find: (1) the probability that a randomly drawn observation from that distrubution is below some value, above some value, or between particular two values (2) The values of the variable of interest that divides the distribution in certain proportions.

Practical Example 1: Find the probability that in a population with normally distributed Weight with Mean = m and SD = s, a randomly drawn individual will have a weight > X.

Practical Example 2: In the same population, in which range of weights do the heaviest q percent individuals fall?

The shiny app presented here, is a tool for solving each of those problems for Normal distributions with the mean between 1 and 100. It can be useful for:

• Practical purposes when calculating Normal probabilities/Finding values for given probabilities is needed
• Learners of statistics to understand the Normal distributions and how to use it to solve practical problems that involve Normal distributions

The app consists of two parts (presented in separate tabs) dedicated to solving each of the two discussed problems: (1) Tab 1: dedicated to finding Normal proportions (probabilities) given values of a Normal variable, (2) Tab 2: dedicated to finding the values of a Normal variablem which are associated with the probabilities of interest.

Besides making calculation and finding the requred values, each tab draws the original distribution with the specified parameters and, in addition to that, draws the Standard Normal distrubution shading the areas corresponding to the parameters of the problem.

At the top of each tab, the app draws the original distribution with the specified parameters. It also shades the corresponding area of the distribution. The example below shows the Normal distribution with Mean = 60 and SD = 15:

The question being answered here is “what is the probability that a random observation from this distribution is below 60?” Half of the distribution is shaded to show that the sought probability is 50%.

The following graph shows the corresponding standard normal distribution, one-half of which is shaded on the left:

This figure allows the user to understand the connection between the values in the original units of measurement and z-scores, since the standardized distribution shows z-scores instead of the original units on the horisontal axis.

Hope you enjoyed messing with the app!