Question

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” or “other.”

Short answer

The given situation can be approximated using the binomial distribution as the outcome of the question asked has exactly two possible outcomes (yes/other), and all the other assumptions are met by the procedure.

Step-by-step solution

Given information

The question asked in the survey is, “Whether the abbreviations like ‘LOL’ and ‘BFF’ are annoying?”

Out of 500 smartphone users who were surveyed, the response to a question had exactly two possible outcomes: “yes” or “other.”

Assumptions of binomial distribution

The assumptions of the binomial distribution that need to be satisfied are given as follows:

• Fixed number of trials.
• The trials should be independent.
• Each trial should have exactly two plausible outcomes: success and failure.
• The probability of success should be the same for all the trials.

Fulfilment of assumptions

The number of trials is fixed and holds a value equal to 500.

All trials are independent, as 500 different users are asked to record their responses.

It can be seen that the trial involves recording the responses of the users. Moreover, the response to the question is of exactly two kinds: “yes” or “other.”

Since all the 500 users have answered the same question, the probability of success will remain the same for all trials.

Since the procedure follows all the above assumptions,the given situation can be modeled using the binomial distribution.