Respuesta :
Using the binomial distribution, it is found that the standard deviation is of 0.9, which means that in most samples of four adults who are late for work, the average number of adults that blame oversleeping would differ from the mean by no more than 0.9.
For each employee there are only two possible outcomes, either they blame oversleeping for being late, or they do not. The answer of each employee is independent of other employees, hence the binomial distribution is used to solve this question.
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
- 28% of U.S. employees who are late for work blame oversleeping, hence p = 0.28.
- You randomly select four U.S. employees who are late for work, hence n = 4.
The standard deviation is of:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{4(0.28)(0.72) = 0.9[/tex]
Which means that in most samples of four adults who are late for work, the average number of adults that blame oversleeping would differ from the mean by no more than 0.9.
More can be learned about the binomial distribution at https://brainly.com/question/14424710
