Question

1. Create 20 random numbers from a binomial distribution of 500 trials and the p-value of 0.4. Draw
a distribution graph of these numbers. How does the distribution look like? Is the central limit
theorem held true in this case? Why or why not? Now, increase the sample size to 100 and
repeat the same process. Is the central limit theorem held true in this case? Why or why not?
Explain using evidence.

Answer 1

R-code:

>x<-rbinom(20,500,0.4)
> plot(density(x))

It is clear from the graph that it does not look like the normal distribution graph.hence this is not held the central limit theorem due to small sample size. because here we have only 20 points which is very less.generally we define n as large no. when it is more than 30.

> y<-rbinom(100,500,0.4)
> plot(density(y))

It is clear from the graph that it is close to the normal distribution graph.hence this is held the central limit theorem .since here we have sample size more than 30.