Question

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Surveying 83 people to determine which brand of apparel is their favorite.

Answer 1

Whether surveying 83 people results in a binomial distribution depends on meeting three conditions: a fixed number of trials, two outcomes (success or failure), and independence among trials. If a favorite brand is defined as 'success,' the other brand as 'failure,' and each choice is independent and equally likely, it could be binomial.

Step-by-step explanation:

To determine whether a procedure results in a binomial distribution, the procedure must satisfy three conditions:

1. There is a fixed number of trials (n).
2. There are only two outcomes: success or failure, for each trial.
3. The trials are independent and repeated under identical conditions.

In the case of surveying 83 people to determine their favorite brand of apparel, these conditions can be met if we define 'success' as selecting a favorite brand and 'failure' as not selecting that brand. The number of trials is fixed at 83, and if each person makes an independent choice with the same likelihood of choosing the brand, and if the probability of success remains constant, then the conditions for a binomial experiment are met. However, if there are more than two brands to choose from, the experiment might not have a binomial distribution due to the second condition not being met.