Question

After being rejected for employment, Kim Kelly learns that Bellevue credit company has hired only five women among the last 17 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 change of gender discrimination by finding the probability of getting five or fewer women when 17people hired assuming that there is no discrimination based on gender

Report answer accurate to 8 decimals places

P(at most five)

Yes this support a charge of gender discrimination

No this doesn't support a change of gender discrimination

Answer 1

• Here, n = 17, p = 0.5, (1 - p) = 0.5 and x = 5
  As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

  We need to calculate P(X <= 5).
  P(X <= 5) = (17C0 * 0.5^0 * 0.5^17) + (17C1 * 0.5^1 * 0.5^16) + (17C2 * 0.5^2 * 0.5^15) + (17C3 * 0.5^3 * 0.5^14) + (17C4 * 0.5^4 * 0.5^13)+(17C4 * 0.5^5 * 0.5^12)
  P(X <= 5) = 0.00000763 + 0.0001297 + 0.0010376 + 0.00518799 + 0.01815796 +0.047211
  P(X <= 5) = 0.02452088

  P(at most five) = 0.071732

  As the value is greater than 0.05%
  No, this does not support a change of gender discrimination

  Option B

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