SOLUTION: After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 16 new employees. She also learns that the pool of a

Question 1152964: After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 16 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting four or fewer women when 16 people are hired, assuming that there is no discrimination based on gender.
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.

            It is a binomial distribution type problem.

            I will use the Excel standard function BINOM.DIST to facilitate calculations.
            It has the analogue --- the standard function binompdf in pocket calculators TI-83 and TI-84.

Probability of hiring 4 or fewer women in 16 position is (assuming equal probability of men and women for each position) 


    P = P(0) + P(1) + P(2) + P(3) + P(4) =  = BINOM.DIST(4, 16, 0.5, TRUE) = 0.0384 = 3.84%.


The Excel standard function BINOM.DIST allows calculating this sum in one click.

Solved.

On Excel function BINOM.DIST, see its description everywhere, for example
https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c

On binompdf function for pocket calculators TI-83 and TI-84 see the link
http://users.rowan.edu/~schultzl/ti/binomial.pdf

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If you want to see other similar solved problems, look into the lessons
    - Solving problems on Binomial distribution
    - How to calculate Binomial probabilities using Technology
    - Solving problems on Binomial distribution with Technology
in this site.

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