Question
5: 5.2 HW 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. Recording the number of televisions in 20 households Choose the correct answer below. A. It is binomial or can be treated as binomial. 1 of 22 points 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 not remain the same in all trials.
Ask by Bush Curry. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
It is not binomial because there are more than two possible outcomes.
Solution
The procedure involves recording the number of televisions in 20 households, and each household could have 0, 1, 2, … televisions. In a binomial experiment each trial must have only two possible outcomes (success or failure). Since here there are more than two outcomes, the experiment does not satisfy the binary outcome requirement.
Thus, the correct answer is:
C. It is not binomial because there are more than two possible outcomes.
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A. It is binomial or can be treated as binomial. In this scenario, the procedure of recording the number of televisions in 20 households satisfies the binomial requirements because there are two clear outcomes: either a household has a television (success) or it does not (failure). Each household can be considered an independent trial, and assuming the total number of households is large, we can apply the \(5\%\) guideline without worrying about changing probabilities.
