Question

After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only two women among the last 20 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 two or fewer women when 20 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most two) = Incorrect
Because this is a serious claim, we will use a stricter cutoff value for unusual events. We will use 0.5% as the cutoff value (1 in 200 chance of happening by chance). With this in mind, does the resulting probability really support such a charge?
no, this does not support a charge of gender discrimination
yes, this supports a charge of gender discrimination

Answer 1

Binomial Problem with n = 20 and p(hire woman) = 1/2

P(at most two) = binomial(20,1/2,2) = 0.0001811

Explanation:

The probability of successes in trials where is the probability of success on any given trial is given by: