My shiny application is a simple way to prove Central Limit Theorem. You can observe as many as you want samples generated by R algorithm that will prove CLT.

library(shiny)


shinyUI(fluidPage(

    # Application title
    titlePanel("Central Limit Theorem Test"),

    # Sidebar with a slider input for number of obs
    sidebarLayout(
        sidebarPanel(
            sliderInput("observations",
                        "Enter the number of observation",
                        min = 1,
                        max = 500,
                        value = 10),
            sliderInput("mean",
                        "Enter the mean.",
                        min = 1,
                        max = 500,
                        value = 10),
            
            textOutput("Theoremstatement"),
            
        ),

        # Show a plot of the generated distribution
        mainPanel(
            plotOutput("distPlot"),
            textOutput("statement")
        )
    )
))

library(shiny)

# Define server logic required to draw a histogram
shinyServer(function(input, output) {
    
    dd <- reactive({rnorm(input$observations, input$mean)})
    actualmean <-reactive({ mean(dd())})
    output$distPlot <- renderPlot({
        
        #dd <- rnorm(input$observations, input$mean)
        #actualmean <- mean(dd)
        aa <- dd()
        hist(aa)
        abline(v = actualmean(), col = "blue")
        abline(v = input$mean, col = "red")
        
    })
    
    output$Theoremstatement <- renderText("          The CLT states that the more observations the closer the actual mean gets to theoretical mean          ")
    
    output$statement <- reactive({
        paste("The theoretical mean is ", input$mean," and the actual mean is", actualmean()," and the difference is ", abs(input$mean - actualmean()))
    })
    
    
    
})

All you have to do is just to choose the number of observation and the theorethical mean value. After that a graph will be presented with 2 vertical lines. The Blue like represents actual mean and the red line represents theoretical mean.