
979 F.Supp. 693 (1997)
Sheila BEW, Rainier Conley, Walter Griffin, Sergintha Hill-Pratt, Samuel Ingram, Barbara Muse, Jean A. Moore, and Vicki Shy, Plaintiffs,
v.
CITY OF CHICAGO, Defendant.
No. 96 C 1488.
United States District Court, N.D. Illinois, Eastern Division.
September 29, 1997.
*694 Kenneth N. Flaxman, Kenneth N. Flaxman, P.C., Chicago, IL, for Plaintiffs.
Susan S. Sher, Patrick J. Rocks, Jr., Shona B. Glink, Jay Michael Kertez, City of Chicago, Law Dept., Corp. Counsel, Chicago, IL, for Defendant.

MEMORANDUM OPINION AND ORDER
BUCKLO, District Judge.
The African-American plaintiffs, Sheila Bew, Rainier Conley, Walter Griffin, Sergintha Will-Pratt, Samuel Ingram, Barbara Muse, Jean Moore,[1] and Vicki Shy, were Chicago probationary police officers.[2] The City discharged them because of their inability to pass the Illinois Law Enforcement Officers Certification Examination ("Certification Examination"). The plaintiffs claim that the exam has a disparate impact on the minority probationary police officers, in violation of Title VII of the Civil Rights Act. 42 U.S.C. § 2000e et seq. The defendant has moved for summary judgement, arguing that some of the plaintiffs have failed to exhaust administrative remedies and that all have failed to provide statistical evidence sufficient to establish a prima facie case of disparate impact. For the following reasons, the motion is denied.

I.
Prior to filing a Title VII suit, the plaintiff must exhaust administrative remedies. First, she must file a charge with the Equal Employment Opportunity Commission (EEOC) within 300 days of the alleged unlawful employment practices. Gilardi v. Schroeder, 833 F.2d 1226, 1229-32 (7th Cir. 1987). Upon receipt of an EEOC Right-to-Sue letter, the plaintiff must file suit within 90 days. Id. at 1233; 42 U.S.C. § 2000e-5(f)(1).
The defendant asserts that Mr. Conley and Ms. Bew never filed EEOC charges. However, the plaintiffs have submitted copies of the EEOC charges filed by these individuals on May 11, 1995 and May 5, 1995, respectively, *695 within the required period after their employment was terminated. The plaintiffs have also submitted a copy of a June 30, 1996 Request for Notice of Right to Sue, transmitted by the Chicago EEOC office to the U.S. Department of Justice, listing Mr. Conley and Ms. Bew as charging parties. The present suit was filed on March 14, 1996. Therefore, the plaintiffs timely exhausted their administrative remedies.[3]

II.
To make out a prima facie case of disparate impact, the plaintiff must show "that the tests in question select applicants for hire or promotion in a racial pattern significantly different from that of the pool of applicants." Albemarle Paper Co. v. Moody, 422 U.S. 405, 425, 95 S.Ct. 2362, 2375, 45 L.Ed.2d 280 (1975). The plaintiff "`must begin by identifying the specific employment practice that is challenged'." Wards Cove Packing Co. v. Atonio, 490 U.S. 642, 656, 109 S.Ct. 2115, 2124, 104 L.Ed.2d 733 (1989) (quoting Watson v. Fort Worth Bank & Trust, 487 U.S. 977, 994, 108 S.Ct. 2777, 2788-89, 101 L.Ed.2d 827 (1988)). The employment practice at issue is the Certification Examination; upon failing this exam, a probationary police officer is fired.
"Once the employment practice ... has been identified, causation must be proved; that is, the plaintiff must offer statistical evidence of a kind and degree sufficient to show that the practice in question has caused the exclusion of applicants for jobs or promotions because of their membership in a protected group." Watson, 487 U.S. at 994, 108 S.Ct. at 2788-89.[4] The plaintiff may demonstrate that "statistical disparities [are] sufficiently substantial [to] raise ... an inference of causation" through standard deviation analysis. Id. at 995 & n. 3, 108 S.Ct. at 2789 & n. 3. This analysis determines whether the disparity at issue is likely to have resulted from chance. Coates v. Johnson & Johnson, 756 F.2d 524, 536-37 n. 11 (7th Cir.1985).
For statistical evidence to be probative, it must be drawn from the correct pool or sample. Wards Cove Packing Co., 490 U.S. at 650-51, 109 S.Ct. at 2121-22. When a test operates as a pass-fail barrier, as is the case here, the proper pool consists of those taking the test. See Connecticut v. Teal, 457 U.S. 440, 442-44, 452, 102 S.Ct. 2525, 2528-29, 73 L.Ed.2d 130 (1982). The parties agree that the pool here properly consists of 4071 majority and minority probationary police officers who took the Certification Examination between 1990 to 1996. The undisputed data in the present case are summarized in the following table:


  ===================================================
              Pass  Fail  Total  Pass Rate  Fail Rate
  ---------------------------------------------------
  Minorities  1965   28   1993   1965/1993   28/1993
  ---------------------------------------------------
  Whites      2077    1   2078   2077/2078    1/2078
  ---------------------------------------------------
  Total       4042   29   4071   4042/4071   29/4071
  ===================================================

Relying on Hazelwood Sch. Dist. v. United States, 433 U.S. 299, 308 n. 14, 97 S.Ct. 2736, 2742 n. 14, 53 L.Ed.2d 768 (1977), and Castaneda v. Partida, 430 U.S. 482, 496-97 n. 17, 97 S.Ct. 1272, 1281 n. 17, 51 L.Ed.2d 498 (1977), the plaintiffs employed standard deviation *696 analysis and compared the observed and the expected number of minority failures.[5]
Unfortunately, the particular statistical technique employed by the Court in Castaneda and Hazelwood cannot be applied to cases [such as the one at bar] concerning ... differences in pass-fail rates in employment tests. The [plaintiffs' method] is appropriate when evaluating the likelihood of a result composed of a series of events, each with only two possible outcomes, such as the selection of either a black or a white from the relevant population ....
Elaine W. Shoben, Differential Pass-Fail Rates in Employment Testing, 91 Harv. L.Rev. 793, 795-96 (1978). The present problem, however, has four possible outcomes  a majority probationary police officer passing and failing and a minority passing and failing. Therefore, a statistical technique known as the test for differences between independent proportions is appropriate. Mack A. Player, Employment Discrimination Law at 365 (1988) (citing Shoben, supra).
The test for differences between independent proportions yields a Z-score of over five standard deviations.[6] The disparity between the minority and the majority pass rates is statistically significant. Therefore, the data support a prima facie case of disparate impact. See Castaneda, 430 U.S. at 496 & n. 17, 97 S.Ct. at 1281 & n. 17 (prima facie case established where Z-score is greater than two or three standard deviations).
The City counters by comparing the pass rates of minorities and nonminorities using the "4/5th rule." The EEOC guidelines provide that "[a] selection rate for any race ... which is less than four-fifth (4/5) (or eighty percent) of the rate for the group with the highest rate will generally be regarded ... as evidence of adverse impact." 29 C.F.R. § 1607.4(D). The defendant's results, which the plaintiffs do not dispute, are as follows: the pass rate for the majority probationary police officers taking the exam is 99.95 percent. The pass rate for African-Americans is 98.11 percent. The pass rate for Latinos is 99.50 percent. The ratio of the African-American to the majority pass rate is 98.16 percent. The ratio of the Latino to the majority pass rate is 99.55 percent.
The "4/5th rule" is merely a "rule of thumb." Watson, 487 U.S. at 995-96 n. 3, 108 S.Ct. at 2789 n. 3. The EEOC guidelines are not binding on the courts. Aguilera v. Cook County Police & Corrections Merit Bd., 760 F.2d 844, 847 (7th Cir.1985). The "4/5th rule" has been criticized by the courts and commentators, Watson, 487 U.S. at 995-96 n. 3, 108 S.Ct. at 2789 n. 3 (citing sources), as "insensitive ... to the magnitude of the difference *697 in treatment of the two groups[, and] ... quite sensitive to the particular framing of the issue and, as a result, ... easily ... misunderstood and misapplied." Paetzold & Willborn, supra, § 5.06, at 5-10 to 5-11. The EEOC itself recognizes that "[s]maller differences [than twenty percent] in selection rate may nevertheless constitute adverse impact, where they are significant in both statistical and practical terms." 29 C.F.R. § 1607.4(D).
In the present case, the analysis adopted by the court is designed to determine whether the disparity between the minority and the majority pass rates, yielded by the "4/5th rule," is statistically significant or, put another way, likely to be due to chance. The fact that the difference between the minority and the majority Certification Examination pass rates exceeds three standard deviations argues against chance. See Hazelwood Sch. Dist., 433 U.S. at 308 n. 14, 97 S.Ct. at 2742 n. 14 (citing Castaneda, 430 U.S. at 496-97 n. 17, 97 S.Ct. at 1281 n. 17) (hypothesis that disparity is due to chance is suspect if Z-score is greater than two or three standard deviations). "Plaintiffs should have the option ... of demonstrating [disparate] impact by statistical significance instead of the four-fifth rule.... [and] where the four-fifth rule indicates lack of [disparate] impact[,] but the disparity is statistically significant, the plaintiff should be able to establish [disparate] impact on the evidence of statistical significance." Paetzold & Willborn, supra, § 5.07, at 5-19 to 5-20.

Conclusion
For the reasons stated above, the defendant's motion for summary judgment is denied. Ms. Bew and Mr. Conley are given 20 days to submit copies of their Right-to-Sue letters.
NOTES
[1]  Jean A. Moore was named in the complaint by mistake. Accordingly, her complaint is dismissed.
[2]  The following facts are undisputed. The defendant asks me to deem admitted certain of its 12(M) Statement facts. I address this issue in a separate minute order.
[3]  The complaint alleges and I assume for the purposes of this motion that Ms. Bew and Mr. Conley actually received their Right-to-Sue letters. However, given the date of the request of the Right-to-Sue letters, June 30, 1996, it appears that the suit commenced before the letters were issued. This fact does not undermine the exhaustion of administrative remedies. See Plummer v. Chicago Journeyman Plumbers, 452 F.Supp. 1127, 1139-40 (N.D.Ill.1978), rev'd on other grounds, Eggleston v. Chicago Journeymen Plumbers, 657 F.2d 890 (7th Cir.1981). Ms. Bew and Mr. Conley are given 20 days to submit copies of their Right-to-Sue letters.
[4]  If the plaintiff makes out a prima facie case of disparate impact, the burden of producing evidence shifts to the defendant. Wards Cove Packing Co., 490 U.S. at 658, 109 S.Ct. at 2125. At this juncture, the City argues only that the plaintiffs have failed to establish a prima facie case that the Certification Examination has a disparate impact on minority probationary police officers.
[5]  Specifically, the parties agree that 49 percent (1993 divided by 4071) of the probationary police officers who took the test are minority. Therefore, the expected number of minorities among the 29 test takers who failed is 14.21 (.49 times 29). The actual or observed number of minority failures is 28. The difference between the observed and the expected number is 13.79. The standard deviation of the observed from the expected is approximately 2.7 [square root of the following: total number in the sample, 29 failures, times the representation of minority test takers (1993 divided by 4071 or .49), times the representation of majority test takers (2078 divided by 4071 or .51)]. The difference between the expected and the observed number of minority failures is 13.79 divided by 2.7 or 5.11 standard deviations.
[6]  The statistical calculation can be done either of two ways, but the result is the same. Compare Player, supra, at 365 with Ramona L. Paetzold & Steven L. Willborn, The Statistics of Discrimination § 5.07, at 5-14 to 5-15 (1994). I have utilized the method described in Paetzold & Willborn. The minority pass rate (Pmi) is 1965 divided by 1993 (.98595); the majority (Pmj) is 2077 divided by 2078 (.99952). The number of minority probationary police officers who took the test is Nmi (1993) and of the majority probationary police officers, Nmj (2078). The total actual pass rate is 4042 divided by 4071 (.99288); the total actual fail rate is 29 divided by 4071 (.00712). The number of standard deviations, or the Z-score, by which the minority pass rate differs from the majority pass rate is calculated as follows:

 [Pmi minus Pmi] divided by the square root of [(total actual pass rate) times (total actual fail rate) times (1/Nmj plus 1/Nmi)]
 [.98595  .99952] / [.99288 × .00712 × (1/1993 + 1/2078)]1/2
 Z-score equals -5.148.
Under this analysis, unlike the "4/5th rule," it does not matter whether pass or fail rates are used. Paetzold & Willborn, supra, § 8.04, at 8-13 n. 77; Player, supra, at 364.
