Question

According Statista, the percentage of Americans who use digital banking is 65.3%. 10 Americans are randomly selected and each is asked if s/he uses digital banking. Use this situation to answer the parts below. (a) Recognizing that this is a binomial situation, give the meaning S and F in this context. That is, define what you will classify as a "success" and what you will classify as a "failure" as it refers to using digital banking.

Answer 1

In the given context, a 'success' is an American who uses digital banking, and a 'failure' is one who does not, making the situation suitable for a binomial probability model with n=10 and p=0.653.

Step-by-step explanation:

In a binomial situation, a success (S) is the outcome of interest – in this case, an American who uses digital banking. Conversely, a failure (F) refers to an American that does not use digital banking. If 65.3% of Americans use digital banking, then a randomly selected American who uses digital banking is considered a 'success', and one who doesn't is a 'failure' in terms of a binomial experiment.

Given that 65.3% of Americans use digital banking when we select 10 Americans at random and ask them whether they use digital banking, we assume each selection is independent, and the probability of each 'success' remains constant (65.3%). The number of Americans from this sample that use digital banking will follow a binomial distribution with parameters n=10 (the number of trials) and p=0.653 (the probability of success).