View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework07/stat212-HW07-18.pg

    1 ## DESCRIPTION
    2 ## Statistics: Sampling Distributions
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('statistics', 'sampling distributions','normal sampling distributions')
    6 ## naw tagged this problem.
    7 
    8 ## DBchapter('Random Variables')
    9 ## DBsection()
   10 ## Date('7/01/2005')
   11 ## Author('Nolan A. Wages')
   12 ## Institution('UVA')
   13 ## TitleText1('Statistics for Management and Economics')
   14 ## EditionText1('6')
   15 ## AuthorText1('Keller, Warrack')
   16 ## Section1()
   17 ## Problem1()
   18 
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGnumericalmacros.pl",
   28 "PGstatisticsmacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 ## install_problem_grader(~~&std_problem_grader);
   35 
   36 $n = random(10,20,1);
   37 $mu1 = random(72,77,1);
   38 $sigma1 = random(18,23,1);
   39 $mu2 = random(63,68,1);
   40 $sigma2 = random(19,24,1);
   41 $s1 = ($sigma1)**2;
   42 $s2 = ($sigma2)**2;
   43 $a = random(15,20,1);
   44 $b = -($mu1-$mu2);
   45 $c1 = ($s1+$s2)**(0.5);
   46 $z1 = $b/$c1;
   47 $c2 = (($s1/5)+($s2/5))**(0.5);
   48 $z2 = $b/$c2;
   49 
   50 BEGIN_TEXT
   51 $PAR
   52 A factory's worker productivity is normally distributed.
   53 One worker produces an average of $mu1 units per day
   54 with a standard deviation of $sigma1.  Another worker
   55 produces at an average rate of $mu2 units per day with
   56 a standard deviation of $sigma2.
   57 $PAR
   58 A.  What is the probability that in a single day worker
   59 1 will outproduce worker 2?
   60 $PAR
   61 Probability = \{ans_rule(15)\}
   62 $PAR
   63 B.  What is the probability that during one week
   64 (5 working days), worker 1 will outproduce worker 2?
   65 $PAR
   66 Probability = \{ans_rule(15)\}
   67 $PAR
   68 
   69 $PAR
   70 
   71 
   72 END_TEXT
   73 
   74 $ans1 = normal_prob($z1,'infty',mean=>0, deviation =>1);
   75 $ans2 = normal_prob($z2,'infty',mean=>0, deviation =>1);
   76 ANS(num_cmp($ans1));
   77 ANS(num_cmp($ans2));
   78 
   79 
   80 
   81 
   82 ENDDOCUMENT();       # This should be the last executable line in the problem.