binomial-variable

The customers at a local appliance store are polled as they leave the store. Each is asked, “What brand of appliance do you prefer?” The random variable x to be reported is whether the appliance brand is Frigidaire. Is x a binomial variable? Justify your answer. Hint: There are four requirements for a binomial probability: 1. There are a fixed number of trials. 2. Each trial can only have two outcomes—success or failure. 3. The outcome of each trial must be independent of each other. 4. The probability of a success must remain the same for each trial. Example In a recent study in England, researchers set out to determine whether dogs could be trained to detect cancer in urine samples. Dogs were trained over six months to select cancer-unique elements in urine samples from patients with bladder cancer, from people who were sick with unrelated diseases, and from healthy people. The researchers found the success rate to be 41% (AP, 2004).. The above is an example of a binomial situation. There are two outcomes—success or failure. In this case, success would be identified when a dog correctly detects the cancerous urine sample. The probability of success is the same for each trial, and the outcome of each trial is independent of each other.