After being rejected for employment, Kim Kelly learns that the
Bellevue Credit Company has hired only five women among the last 22
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 five or fewer women when 22 people are
hired, assuming that there is no discrimination based on
gender.
(Report answer accurate to 8 decimal places).
P(at most five) =
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?
Answer:
Given,
sample n = 22
Binomial distribution P(X = r) = nCr*p^r*q^(n-r)
nCr = n!/(n-r)!*r!
p = 0.5
P(At most 5) = P(X <= 5)
= P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) P(x = 4) + P(x = 5)
= 22C0*0.5^0*0.5^22 + 22C1*0.5^1*0.5^21 + 22C2*0.5^2*0.5^20 + 22C3*0.5^3*0.5^19 + 22C4*0.5^4*0.5^18 + 22C5*0.5^5*0.5^17
= 0.00000024 + 0.000005 + 0.000055 + 0.00037 + 0.0017 + 0.0063
= 0.0084
Probability = 0.0084
Here we can say that, the probability is greater than 0.005 , so we don't support a charge of gender discrimination.
Option B.
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