Assignment 2 Quantitative Methods IIshita KayasthaSection D, Roll No. 1411232Problem 1The lot has 200 radios, out of which Shankar inspects 4 radios to determine whether to acceptor reject the lot.a) the proportion of defectie pieces in the lot is 10 %. b) the proportion of defectie pieces !1 considered are 15%, 20% & 25%. To find the probabilit" of a wron# rejection, we find the probabilit" of how man" times the rule would actuall" be satisfied $i.e the minimum no. % would be defectie) #ien the ma&imum state of a #ood population $i.e when !1 ' of the population is defectie)To find the probabilit" of a wron# acceptance, we first find the probabilit" of how man" times the rejection rule would be satisfied at the minimum state of a bad population $once a#ain, at !1 ' of population is defectie). (e then subtract this from 1, to find out the probabilit" of acceptance in case of such a rule.The solution for both parts $a) and $b) is #ien in the followin# )&4 table*+eject if there are atleast & in the sampleare defectieProbabilit"$(ron# rejection)Probabilit" $(ron# ,cceptance)at !1 - 1)'Probabilit" $(ron# ,cceptance)at !1 - 20'Probabilit" $(ron# ,cceptance)at !1 - 2)'& - 0 1 0.000 0.000 0.000& - 1 0..4/ 0.)10 0.40/ 0..1.& - 2 0.0)1 0.102 0.121 0.2.0& - . 0.00. 0.010 0.024 0.0)1& - 4 0.000 0.000 0.000 0.00/1Problem 2The alues taken are n p a b c d2.2 0.)0 110 120 1.0 1403ean - 116Standard deiation - 7.615773114or the normal appro&imation, the followin# continuit" corrections hae been made* $%5a)*- The normal appro&imation is calculated at P$%5100.)), since 110 is not included in the binomial distribution$b5%5-c)*- The 6ormal appro&imation is calculated at P $120.)5%5-1.0.)), since 120 is notincluded and 1.0 is included in the binomial distribution. $%7-d)*- The 6ormal appro&imation is calculated at P $%7-1.0.)), since 140 is included in the binomial distribution.The 8inomial Probabilities and the 6ormal ,ppro&imations are #ien below*9&act $8inomial)6ormal,ppro&imation ,bsolute ' :ifference%$5a) 0.10/21/002 0.10/2 0.01%$b5%-5c) 0.24000)10) 0.2411 0.01%$7-d) 0.00001.11. 0.0010 1.22Thus, it can be obsered that the absolute percenta#e difference between the e&act or binomial probabilit" and the correspondin# 6ormal ,ppro&imation is less than 2 percent for the aboe calculations. This indicates that the appro&imation can be effectiel" used to modelthe binomial distribution. (e can also see the appro&imation is most accurate at alues closer to the mean, and this accurac" decreases towards the e&tremes. This can be attributed to the fact that the 6ormal :istribution is infinite in both tails ; thus has infinite ran#e, while the binomial distribution has a finite ran#e. Thus, while appro&imatin# a continuous distribution to a discrete distribution, a mar#inal difference comes in.2Problem .The stocks selected for the portfolio are Cipla, HDFC Bank, Infosys & Z.Time hori