In Exercises 5–12, determine whether the given procedure resul...

Question

In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.

Pew Survey In a Pew Research Center survey of 3930 subjects, the ages of the respondents are recorded.

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.”

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Identify whether the situation follows a binomial distribution or if it can be treated as a binomial using the 5% rule for cumbersome calculations. During a market research survey, 300 consumers were asked if they prefer traditional shopping or online shopping, with possible answers being prefer traditional, prefer online, or no strong preference. Awesome. So it appears for this particular prong, we're asked to identify whether or not the situation that is provided to us by the prom itself follows a binomial distribution, or if it can be treated as a binomial using the 5% rule for cumbersome calculations. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is the situation follows a binomial distribution. B is the situation can be treated as a binomial distribution using the 5% rule for cumbersome calculations. C is the situation does not follow a binomial distribution and cannot be treated as one, and D is cannot be determined. Awesome. So first off, in order to determine if the situation follows a binomial distribution, or if it can be treated as a binomial using the 5% rule for cumbersome calculations, let us review the criteria, as we should recall, for a binomial distribution. So firstly, A fixed number of trials. So we need to determine whether or not the number of trials N is fixed. Secondly, two possible outcomes. So each trial has only 2 possible outcomes. 3, thirdly, Constant probability of success, we need to note that the probability of success P is the same for each trial. And finally, fourthly, independent trials. The outcome of any of any individual trial is independent of the outcome of any other trial. So, With that in mind, we need to check whether the situation meets the criteria for binomial distribution. So first, let's focus on the condition for the fixed number of trials. So we're told that there are 300 consumers being surveyed, so the number of trials is fixed. So I'll use a checkmark to denote it is fixed. So now, our second thing we need to consider is the two possible outcomes. Each trial has only 2 possible outcomes. So for this particular problem, there we need to note that there are 3 possible answers. Because on the survey they have prefer traditional, prefer online, and no strong preference. So there's 3 possible answers, not 2, and this does not meet the binomial distribution criterion. Of having only two outcomes, so since the situation has already failed the criteria for number 2, this particular situation does not follow a binomial distribution and cannot be treated as one, so it does not have two outcomes. And because of that, our final answer, without a doubt has to be multiple choice answer letter C, which once again is the situation does not follow a binomial distribution and cannot be treated as one. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Binomial Distribution

5% Guideline

Requirements for Binomial Distribution

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