Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

LOL In a U.S. Cellular survey of 500 smartphone users, subjects are asked if they find abbreviations (such as LOL or BFF) annoying, and each response was recorded as “yes,” “no,” or “not sure.”

The question asked in the survey is, “Whether the subjects find abbreviations annoying or not?”.

Out of 500 smartphone users who were surveyed, the response to a question had more than two possible outcomes: “yes,” “no,” and “not sure.”

The following assumptions of the binomial distribution should be satisfied:

• Finite and independent trials
• Two possible outcomes (success and failure) for each trial
• The probability of success should be the same for each of the trials

Out of the given set of assumptions required for a procedure to follow the binomial distribution,one such assumption is that the outcomes of the event whose probability is to be computed should be of exactly two kinds:

• One outcome is considered as the success;
• The remaining outcome is considered afailure.

Here, the answer to the question of whether the subject finds abbreviations annoying or not has more than two possible outcomes (“yes,”“no,” and “not sure”).

Therefore, the given situation cannot be modeled using the binomial distribution.