Question

Using technology, roll 100 virtual dice and find the sum of their values. Do this 200 times and plot the sums. What does the shape of this sampling distribution approximate? Explain the relation of the Central Limit Theorem to this problem. Organize this activity into a lesson plan format and allow the students opportunities to investigate with dice.

Answer 1

we can solve this using R , as shown below

set.seed(1)
# get sum of 100 dice rolls
sum100dice <- function(){
n=100
x <- replicate(n, sample(1:6, n, replace=TRUE), simplify='vector')
sum(x==6)
}
sum100dice() #these come out as expected

sum200 <- replicate(200,sum100dice(),simplify='vector')
sum200

hist(sum200,col="red",main=" 200 times")

## increase this

sum1000 <- replicate(1000,sum100dice(),simplify='vector')

hist(sum1000,col="steelblue",main=" 1000 times")

the results are

as you increase the repetitions the shape would be closer to normal , in accordance with the central limit theorem