View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework04/stat212-HW04-13.pg

    1 ## DESCRIPTION
    2 ##  Statistics: Probability
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('statistics', 'probability')
    6 ## naw tagged this problem.
    7 
    8 ## DBchapter('Probability')
    9 ## DBsection()
   10 ## Date('6/13/2005')
   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 
   33 
   34 
   35 TEXT(beginproblem());
   36 $showPartialCorrectAnswers = 1;  # Change to 0 to shut off separate answer display.
   37 ## install_problem_grader(~~&std_problem_grader); # Uncomment to turn off partial credit.
   38 
   39 
   40 $a = random(.50,.60,.01);
   41 $b = random(.70,.80,.01);
   42 $c = random(.80,.90,.01);
   43 
   44 BEGIN_TEXT
   45 $PAR
   46 The chartered financial analyst (CFA) is a designation
   47 earned after taking three annual exams (CFA I,II, and III).
   48 The exams are taken in early June.  Candidates who pass
   49 an exam are eligible to take the exam for the next level
   50 in the following year.  The pass rates for levels I, II,
   51 and III are $a, $b, and $c, respectively.  Suppose that
   52 3,000 candidates take the level I exam, 2,500 take the
   53 level II exam and 2,000 take the level III exam.  A randomly
   54 selected candidate who took a CFA exam tells you that he
   55 has passed the exam.  What is the probability that he
   56 took the CFA I exam?
   57 $PAR
   58 Probability = \{ans_rule(15)\}
   59 
   60 $BR
   61 
   62 END_TEXT
   63 
   64 &ANS(num_cmp((0.4*$a)/((0.4*$a)+((1/3)*$b)+((2/7.5)*$c))) );
   65 
   66 ENDDOCUMENT();       # This should be the last executable line in the problem.