Extra\tCredit\tAssignment\tBefore\tFinal\tExam Due\tFriday\tDecember\t9,\t2016\t(20\tpoints\ttotal) 1. (3\tpoints) Customers\tof\tan\ton-line\telectronics\tstore\tspend\tan\taverage\tof\t$120\twith\ta standard\tdeviation\tof\t$80\tand\tare\talso\tcharged\ta\tshipping\t&\thandling\tfee\tof\t$5\tper\tpurchase. What\tis\tthe\tchance\tthat\tthe\tnext\t100\tcustomers\twill\tpay\tan\taverage\tof\tmore\tthan\t$128 (including\tthe\tshipping\t&\thandling\tcharges)? 2. (5\tpoints)\tFull\tterm\tpregnancies\tin\tthe\tU.S.\tlast\ta\tmedian\tof\t268\tdays\twith\ta\tstandard deviation\tof\t10\tdays.\tHowever,\tabout\t3%\tof\tdeliveries\tdo\tnot\tgo\tfull\tterm\t(and\tare\tless\tthan 238\tdays). What\tis\tthe\tprobability\tthat\tthe\tmajority\tof\t1000\trandomly\tsampled\tdeliveries\tin the\tU.S.\tare\tless\tthan\t268\tdays? a)\t(0.5\tpoints)\tLet\tVi\tbe\ta\tBernoulli\trandom\tvariable\twhich\t=1\tif\tthe\tith\tfull\tterm\tpregnancy\tis less\tthan\t268\tdays\t(=\t0\totherwise). What\tis\tpi\t=\tP(Vi\t=\t1)? b)\t(1\tpoint)\tLet\tY\t=\thow\tmany\tof\tthe\t1000\tdeliveries\tare\tfull\tterm. What\tis\tthe\tdistribution\tof Y? c)\t(1\tpoint)\tLet\tX\t=\thow\tmany\tof\tthe\t1000\tdeliveries\tinvolve\tpregnancies\tless\tthan\t268\tdays. Explain\twhy = !!!! ! +\t(1000-Y)\t=\t1000 + !!!!(! 1) d)\t(1.5\tpoints)\tFind\tE(X)\tand\tVar(X)\tand\texplain\twhy\tX\tshould\tbe\tapproximately\tnormally distributed. e)\t(1\tpoint)\tFinally,\tfind\tthe\tanswer\tto\tthe\tproblem:\tWhat\tis\tthe\tprobability\tthat\tthe\tmajority of\t1000\trandomly\tsampled\tdeliveries\tin\tthe\tU.S.\tare\tless\tthan\t268\tdays? 3.\t(4\tpoints)\tA\tparking\tlot\tfor\ta\tbaseball\tstadium\thas\ttwo\tentrances.\tIn\tthe\ttwo\thours\tbefore\ta game,\tcars\tenter\tfrom\tthe\tSouth\tentrance\tat\ta\trate\tof\t10\tper\tminute\tand\tfrom\tthe\tNorth entrance,\tindependently,\tat\ta\trate\tof\t20\tper\tminute.\tIt\tis\t30\tminutes\tuntil\tgame\ttime,\twhat\tis the\tdistribution\tof\tthe\ttime\tuntil\tthe\tnext\tcar\tenters\tthe\tlot? 4.\t(4\tpoints)\ta\tlarge\tlab\thas\tthousands\tof\tmice\tthat\tare\thoused\tin\tcages\twith\tfour\tmice\teach. The\tweights\tof\ta\tsingle\trandomly\tchosen\tmouse\tis\t32\tgrams\twith\ta\tstandard\tdeviation\tof\t4 grams.\tOf\tcourse\tmice\tin\tdifferent\tcages\tare\tindependent\tof\teach\tother.\tHowever,\tthe correlation\tbetween\tthe\tweights\tof\ttwo\tmice\tin\tthe\tsame\tcage\tis\t-0.2\t(the\tcorrelation\twithin\ta cage\tis\tslightly\tnegative\tbecause\twhen\tone\tmouse\teats\tmore\tothers\twill\tthen\teat\tless).\tA random\tsample\tof\t20\tcages\tis\tselected.\tWhat\tis\tthe\texpected\tvalue\tand\tstandard\tdeviation\tof the\ttotal\tweight\tof\tthe\t80\tmice\tin\tthose\tcages? 5.\t(4\tpoints:\t0.5\tpoints\teach\tpart)\t30%\tof\tpickup\ttrucks\tin\tState\tCollege\tare\tblack\tand\tthe weight\tof\tblack\tpickup\ttrucks\taverages\t7500\tpounds.\tFor\teach\tof\tthe\tsituations\tbelow\tstate whether\tA\tor\tB\tis\tmore\tlikely;\tor\tdo\tthey\thave\tthe\tsame\tprobability\t(choice\tC)? i) A)\tseeing\tless\tthan\t25%\tof\tthe\tpickups\ton\tan\ton-ramp\tto\tI-99\tbeing\tblack B)\tseeing\tless\tthan\t25%\tof\tthe\tpickups\ton\tI-99\tbeing\tblack ii) A)\tseeing\texactly\t30%\tof\tthe\tpickups\ton\tan\ton-ramp\tto\tI-99\tbeing\tblack B)\tseeing\texactly\t30%\tof\tthe\tpickups\ton\tI-99\tbeing\tblack iii) A)\tseeing\t28\tto\t32%\tof\tthe\tpickups\ton\tan\ton-ramp\tto\tI-99\tbeing\tblack B)\tseeing\t28\tto\t32%\tof\tthe\tpickups\ton\tI-99\tbeing\tblack iv) A)\tseeing\tover\t35\tout\tof\t100\tpickups\ton\tan\ton-ramp\tto\tI-99\tbeing\tblack B)\tseeing\tover\t350\tout\tof\t1000\tof\tthe\tpickups\ton\tI-99\tbeing\tblack v) We\tsee\t5\tpickups\tin\ta\trow\ton\tthe\ton-ramp\tthat\tare\tblack\ton\tI-99 A)\tthe\tnext\tpickup\ton\tthe\ton-ramp\tto\tI-99\tis\tblack B)\tthe\tnext\tpickup\ton\tI-99\tis\tblack vi) A)\tseeing\ta\ttotal\tweight\tof\tover\t80000\tpounds\tfor\t10\tblack\tpickups\ton\tan\ton-ramp\tto\tI-99 B)\tseeing\ta\ttotal\tweight\tof\tover\t800000\tpounds\tfor\t100\tblack\tpickups\ton\tI-99 vii)\tA)\tseeing\tan\taverage\tweight\tbetween\t7000\tand\t8000\tpounds\ttoday\tfor\tblack\tpickups\ton an\ton-\tramp\tto\tI-99 B)\tseeing\tan\taverage\tweight\tbetween\t7000\tand\t8000\tpounds\ttoday\tfor\tblack\tpickups\ton\tI-99 viii)\tA)\tseeing\tan\taverage\tweight\tover\t8000\tpounds\ttoday\tfor\tblack\tpickups\ton\tan\ton-ramp\tto I-99 B)\tseeing\tan\taverage\tweight\tover\t8000\tpounds\ttoday\tfor\tblack\tpickups\ton\tI-99 \f