Question

The “Liars Index” is a nationally recognized statistic reported biannually, indicating the rate of executive résumés that include misrepresented education credentials and/or employment information. The most recently reported Liars index is 24.39%, which means 24.39% of executive job applicants lied on their résumés. if there are 15 résumés for an executive position How many résumés that include misrepresentations do you expect to find? With what standard deviation?

Answer 1

Solution:

Let X be a random variable which represents the number of resumes that includes misrepresentations.

Given that, 24.39% of executive job applicants lied on their resumes.

Let us consider "getting an resume which includes misrepresentations" as success. So, now we have only two outcomes (success and failure).

Then, probability of success (p) = 24.39% = 0.2439

Number of trials (n) = 15

Since, probability of success remains constant in each of the trials, we have only two mutually exclusive outcomes (success and failure), number of trials is finite and the outcomes are independent to each other, therefore we can consider X as binomial distributed random variable.

For binomial distribution the expected value is given as follows:

E(X) = np

Where, p is probability of success and n is number of trials.

We have, n = 15 and p = 0.2439

Hence, E(X) = 15 × 0.2439 = 3.6585

Standard deviation of binomial distribution is given as follows:

Standard deviation is 1.6632.

Hence, we can expect to find 3.6585 resumes with standard deviation of 1.6632, that include misrepresentations.