In: Statistics and Probability
4.) Determine whether the following probability experiment is a binomial experiment. If the probability experiment is not a binomial experiment, state why?
a.) In a town with 400 citizens, 100 randomly selected citizens are asked to identify their religion. The number who identify with a Christian religion is recorded.
b.) An experiment is conducted in which a single die is cast until a 3 comes up. The number of throws required is recorded.
For binomial distribution requirements are :
1) Fixed trials n
2) Only two outcomes on a single trial : success and failure
3) Trials are independent
a) x be the number who identify with a Christian religion is recorded
1) x has only two outcomes , Success : Christian religion and failure : Non Christian religion.
2) Trials are fixed n = 100
3) Citizens are randomly selected so all the trials are independent.
So this probability experiment satisfied all the requirements , so it is a binomial experiment.
b) x be the number of throws required is recorded.
1) x has infinite outcomes : 1,2,3,....
2) Trials are not fixed. ( infinite outcomes )
So this probability experiment does not satisfied the requirements , so it is not a binomial experiment.