Five teachers at Springfield Elementary School are randomly selected without replacement, and the number of years they taught at the school is recorded

Question

1. Not binomial; there is not a fixed number of trials
2. Not binomial; there are more than two outcomes for each trial
3. Not binomial; the trials are not independent
4. Not binomial; for more than one of the reasons given in the above answer choices
5. This procedure results in a binomial distribution

Answer 1

There are fixed number of trials as five teachers are selected.

There could be more than two outcomes for each trial as each teacher can teach 1,2,5 or10 years, so Binomial condition of exactly two outcomes in each trail is violated., hence not a binomial.

The trials are conducted without replacement so they are not independent (the probability is not constant throughout the trials). Hence not a binomial.

So I would go for the fourth option-Not binomial: for more than one of the reasons given in the above choices.

Hope this is helpful.

Answer 2

Hi Tatihana,

Recall that binomial implies two outcomes, success and failure. You do not have that here. It is possible for a teacher to have taught for one, two, five, or ten years. That is not success vs. failure, so it's either choice b or choice d. Let's talk about the other options. Five teachers were selected, and that is a fixed number of trials. Teachers were selected randomly and without replacement, which means each selection is independent of others. So, we have to go with: b. Not binomial because there are more than two outcomes for each trial. I hope this helps.