Question

4.The top 5% of applicants (as measured by GRE scores) will receive scholarships to certain university. GRE scores ~ N(500, 100).

a) If an applicant who took GRE is selected at random, what is the probability that his/her score was more than $520 on that exam?

b) If an SRS of 100 applicants is selected, what is the probability that their average score on GRE is more than $520?

c) 99% of applicant will get between ____ and ____ points on GRE.

d) How high does an applicant’s GRE score have to be to qualify for a scholarship?

Answer 1

- let X denote GREScores لمعلوممكاN ملا Z=x-500 N10,1) loo P(x - 5200 = prx-500 > 520-500 10 loo = P(Z > 0.2 - P(x>520) = 0.4 2074 (using normal Tobles) naloo (samplesize) let X dende average score =x-500 ~NO.D ToolsToo PUX 5201= P(x-500 752-500. I loolioo tooloo = P(231) P(X7520) = 0.15866 (using Mainel Tobles) lie blue let x, ßt denotes the 2 required scores Pla, < X<%) = 0.99 the empirical rule 99% of obscursions 1-35 & u +35. So = 4-30= 500-3(100) = 200 $,= 4+ 30 = 500+ 3(10) = 800 =) 99.1 of applicant will get between [200] and [800] points on GRE hor Scholarship, applicant must be in Topsy PLX>2) = 0.05 where x is required Score to obtain - Pl X-500 > x-500=0.05 scholarship) =) P(Z > 26.0p) = 0,05 - x-500 = 1.645 > la- 6645 (using Namal Tables)