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