Question

10% , the new 20% received the middle % In a large section of the points for the final exam are normally distributed with a man of 72 and a landard deviation of rates are assigned such that the receive the next 20% re s, and the bottom 10 receives. Find the lowest score on the talent would quality a w ent for an A, B, C, anda Gacke .Po to the Standard NormalTable The lowest score at would quality student for an Round up to the nearest Integer as needed) The lowest score that would det for a Round up to the nearest as needed) The lowest score at would quality and for acis Round up to the earlier as needed) The lowest score that would i det for a Round up to the nearesteer as eeded)

Answer 1

nas solution: Let x denote the points for a final exam. Given that is Normally distributed with M= 72,0=9 • A grade is received by top 10 % · B grade is received Ey next 20% .c grade is received by middle 40% D geade is received by next 20% of Irade is received by the bottom 10% (a)ler The cutoff score for getting A be given as a P(x<a) = 0.90 P(x=4 < ar 4) = 0.90 P(zcan)=0.90 where = *-4 ~ N(0,1) $(974= 0.90 ar y = b[0.90) [using standard Normal Area 1 Table a = 1.28x9 +72 = 89.52 ~ 1841 Hence the lowest score that would qualify fore an a es 83.52 ~ '84 a-72 = 1028

by let b be lowest seosee reequiseed to get greade B. P(x<b) = 0.70 P(xu (bok) = 0.70 ( boy) = 0.70 6-92.5 (0.70) 9 6-72 = 0.524 b = 0·524*9) +72 b = 761HG b^[78] Hence students getting b/w 76 716 and 83:52 get a B. e) Similarly, let e be the lowest scores requiseed to get grade P(*<)- 0.30 Play Luc Corn20.30 ( 4) = 0.80 CX-5*(0.39) C-722 0.524 c- (-0.624 xq)+22 - 67.284 => ex 167 Hence students getting bfas 67.284 and 761716 get a c. d) Similarly, if d be lowest scoree to get Grade D, (44) = 0.10 0-72- 5 "(0.10) da 61- 28*9)+2 = 60.48 + d- [60] Hence the students getting b/w 60.48 8 67. 284 get an D. OD

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