Question

Suppose you run an accounting firm and you're concerned about gender discrimination in the hiring process. The hiring process at your firm consists of two stages: review of resumes and then an in-person interview. Imagine that for a particular position your firm gets 120 resumes, 40 of which are from women. Your company will select 20 resumes for the in-person interview. If very few women are selected for the interview stage, it might be due to random chance or it might be due to sexism. (Assume every applicant, regardless of gender, is equally qualified.) To inform you on which it is, you need to know the likelihood that it's due to random chance. Using the appropriate distribution function in Excel, determine the chance of zero women making it to the in-person stage. Express your answer as a decimal to four places. Include a zero before the decimal point.

Answer 1

Solution :

Since there are 40 women applicants and we will we will select them in random, the appropriate distribution strategy will be a random distribution. However, we see that there are basically two outcomes for the selection. A woman can either be selected or not. The probability of a woman being selected is 40/120 = 0.33 and the number of trials is 20. So we can frame the question as

If we select 20 candidates, what is the probability that we will select 0 woman candidates where the probability of selecting a woman candidate is 0.33.

The best suited approach is binomial distribution. The excel formula we will use is

=BIONM.DIST(0,20,0.33,FALSE)

Here 0 denotes the number of occurrence in question, 20 is the number of trials, 0.33 is the general probability and FALSE represent independent events.

The answer is = 0.00033227376617

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