Determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the $5 \%$ guideline for cumbersome calculations). If it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
Randomly selecting 20 citizens of a state and recording their nationalities
Choose the correct answer below.
A. It is binomial or can be treated as binomial.
B. It is not binomial because there are more than two possible outcomes and the trials are not independent.
C. It is not binomial because there are more than two possible outcomes.
D. It is not binomial because the probability of success does notremain the same in all trials.
Answer
\(\boxed{\text{(C) It is not binomial because there are more than two possible outcomes.}}\)
Step 1 ：The binomial distribution has two outcomes: success or failure.
Step 2 ：In this case, the nationality of a citizen can be more than two, so it does not satisfy the requirement of a binomial distribution.
Step 3 ：Also, the probability of each nationality may not be the same, so the probability of success does not remain the same in all trials.
Step 4 ：Therefore, this is not a binomial distribution.
Step 5 ：\(\boxed{\text{(C) It is not binomial because there are more than two possible outcomes.}}\)
