# probability of acceptance

• Aug 2nd 2009, 09:37 PM
skorpiox
probability of employment
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three 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 three or fewer women when 16 people are hired, assuming that there is no discrimination based on gender.

P(at most three) =

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?

I'm a little confused with this exersise ; I used .5% as a probability , 16 as n , and 3 as x using binomial cumulative distribution , but I'm still missing something ( I believe it's the probability!). Can someone help me? thanks in advance!
• Aug 3rd 2009, 04:18 AM
mr fantastic
Quote:

Originally Posted by skorpiox
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three 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 three or fewer women when 16 people are hired, assuming that there is no discrimination based on gender.

P(at most three) =

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?

I'm a little confused with this exersise ; I used .5% as a probability , 16 as n , and 3 as x using binomial cumulative distribution , but I'm still missing something ( I believe it's the probability!). Can someone help me? thanks in advance!

Let X be the random variable number of women chosen.

X ~ Binomial(n = 16, p = 1/2).

Calculate $\displaystyle \Pr(X \leq 3)$. Is it less than 0.005? What conclusion do you draw?
• Aug 3rd 2009, 01:22 PM
skorpiox
thanks mr. fantastic. this probability is equal to .010635376 , which does not support the charge!