Suppose you're working out the policy of admissions for a small, high-powered, very exclusive college. This college is very politically conscious, and carefully screens its incoming class with an eye to make sure it's demographically representative of the population. After filtering out all applications with SAT scores below 2200 (out of a possible 2400), your school is left with 800 qualifying applications.
A problem has come up, though. When looking at the mandatory %26quot;eye color%26quot; fields of the incoming applications, your admissions office has discovered that 15% of your applicants have indicated that they have lightly colored eyes, while 85% have indicated that they have darkly-colored eyes This is a problem, because the general population from which your college draws has 30% light eyes and 70% dark eyes: the light eyed demographic is severely underrepresented among your applicants.
So, your school wishes to implement an affirmative action program that makes your student body more representative of the surrounding population: you aim for a pool of accepted applicants that where 30% have lightly colored eyes and 70% have darkly colored eyes, by changing the minimum cutoffs for SAT scores to different levels for light eyed and dark eyed applicants. You want to have the same number of accepted applications (800) as you currently do. So,
a) What score must the minimum SAT cutoff be lowered to for light-eyed applicants, and what must it be raised to for dark-eyed applicants, to achieve the desired distribution?
b) After implementing the change, what will be the average SAT score for light-eyed students at your college? What will be the average SAT score of dark-eyed students? (Assume that eye color has no impact on SAT performance in the general population.)
c) How does this bear relevance on the idea that affirmative action creates truth to stereotypes that did not exist before?
(i) For the easier version of this problem, assume that the distribution of SAT scores among your applicants is completely even (e.g. pulling an application at random is exactly as likely to produce an SAT score of 1180 as it is one of 2110).
(ii) For the more realistic version (which will require calculus to complete), assume the distribution of SAT scores among your applicants is modeled by a Gaussian distribution centered at 2100 with a standard deviation of 100.A little affirmative action math problem?Stuff the affirmative action, the best 800 get the places, regardless of their eye colour.A little affirmative action math problem?Are.....are you actually getting us to do your homework? *blink*A little affirmative action math problem?If I'm working out the policy for admissions, my drivers are: following the law, not getting sued, and not wasting the school's money. Eye color is not a protected class. Not a protected class, no law suits. Why would I waste my employer's money on promulgating this policy when there's absolutely no risk-mitigation benefit?A little affirmative action math problem?OK here's a guess. I seem to recall that 65-70% of a Gaussian distribution is within 1 SD of the mean, and 95% is within 2 SD of the mean.
Since only 15% of light eyed people scored above 2200, you can guestimate the average score to be about 2100. (i.e. around 15% would be above 2200 and around 15% would be under 2000).
So you need to know confidence interval contains 40% of a Gaussian distribution centred at 2100 and with a SD of 100. Then set the light-eyed standard to the upper end of that interval. I have not taken stats in over 15 years, so I cannot hope to remember. But at one point, this would've been easy.A little affirmative action math problem?20 years ago, this math question would have been right up my alley, lol. Bottom line, accept the most qualified.A little affirmative action math problem?a) surely that depends on the scores people got.
b) same as %26quot;a%26quot;
c) um i don't think it would unless the stereotype was that light eyed people were benefitters of affirmative action
i) ah, this explains %26quot;a%26quot; I still don't know because I don't understand the score system. What is the top mark? oh i see you gave it.
a) 2000
b) um i think (2300*70 + 2200* 30) / 100 = whatever
c) i don't get this part. The fact that they achieved less suggest the stereotype they are stupider is right. Affirmative action just gives them an unfair advantage. Oh no wait, I think I get it, because they will be in a position they shouldn't have been, just like if female doctors were allowed in with less, then the generalisation that female doctors are stupider would be true.
ii) yeah, um am i allowed to look at my notes. It is not possible that my eye coloured peoples follows such a distribution, as not getting the top marks was obviously a freak accident or something, as we are superior, just like rudolf said.
Wait, didn't I already passed this module?
I actually had to google gaussian distribution to find that it was the same thing as normal disrtibution. I should have known cos it was an obvious application. University teaches me to pass tests, not to be useful.A little affirmative action math problem?Austin, shove the affirmative action and the profiling and admit the best possible candidates. No one should be turned down because of someone else's idiosyncrasies.
