Question

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?

Answer 1

Explained below.

Explanation:

A Binomial experiment has the following properties:

• There are a fixed number of trials (n).
• Each trial are independent of the others.
• Each trial has only two outcomes: Success and Failure
• Each trial has the same probability of success (p).

If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.

The number of employees selected is, n = 20.

Every employees response is independent of the others.

Each employees response is either: Yes or No.

The probability of an employee responding as "yes" is, p = 0.31.

Thus, the experiment being performed is a binomial experiment.

So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.

But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.