4.) Determine whether the following probability experiment is a binomial experiment. If the probability experiment is...

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.

Solutions

Expert Solution

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.

orchestra answered 1 year ago

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