Question

determine if the following scenario is a binomial experiment. if it is not binomial, then select all of the reasons why. brand a has a history of recalling 27% of their products. an employee at walmart is going through a list of 54 recalls, and records the number of products being recalled by brand a. the variable is not discrete. there is not a fixed number of trials. there are more than two outcomes. the trials are not independent. the probability of success is not the same for each trial. all of the conditions for being a binomial experiment are met, i.e., this is a binomial experiment.

Explanation:

Step1: Recall binomial experiment conditions

A binomial experiment has 4 conditions: fixed number of trials ($n$), two - outcomes per trial (success/failure), independent trials, and constant probability of success ($p$) for each trial.

Step2: Analyze number of trials

The employee is going through 54 recalls, so $n = 54$ (fixed number of trials).

Step3: Analyze outcomes

There are two outcomes: a product is recalled by Brand A (success) or not recalled by Brand A (failure).

Step4: Analyze independence

The recall of one product does not affect the recall of another product among the 54 recalls, so the trials are independent.

Step5: Analyze probability of success

Brand A has a history of recalling 27% of their products, so $p=0.27$ and it remains the same for each of the 54 trials.

Answer:

All of the conditions for being a binomial experiment are met, i.e., this is a binomial experiment.