According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d)

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=>

Thus

Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as