########################################################################
## DESCRIPTION
## A WeBWorK problem that asks students to find z-scores given the area under the 
## normal curve
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('normal curve', 'area', 'z-score', 'inverse', 'invnorm')
##
## Author('JoAnne Taormina')
## Institution('Nassau Community College')
########################################################################
DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGasu.pl",
"PGnumericalmacros.pl",
"PGstatisticsmacros.pl",
"PGnauGraphics.pl",
"PGnauStats.pl",      
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"weightedGrader.pl",
);

install_weighted_grader();

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(55,90,.01);
$b = random(55,90,.01);
$ans1 = normal_distr(($a-50)/100);

# round $ans1 to 2 decimal places
$ans1 = int(100*$ans1+.5*($ans1 <=> 0))/100;
$diagram1 = DrawNormalDist( -INF, $ans1, "", "z");

$ans2 = normal_distr(($b-50)/100)*(-1);

# round $ans2 to 2 decimal places
$ans2 = int(100*$ans2+.5*($ans2 <=> 0))/100;
$diagram2 = DrawNormalDist( $ans2, INF, "z", "");

$ans1 = Compute($ans1);
$ans2 = Compute($ans2);

BEGIN_TEXT
$BCENTER
\{Plot($diagram1, tex_size=>900);\}
$ECENTER $BR
(a) For a normal distribution, find the z-score that cuts off the bottom $a% of all the z-scores. $BITALIC Round to 2 decimal places after the decimal point.$EITALIC $BR answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram2, tex_size=>900);\}
$ECENTER $BR
(b) For a normal distribution, find the z-score that cuts off the top $b% of area. $BITALIC Round to 2 decimal places after the decimal point.$EITALIC $BR answer: \{ans_rule(10)\} $PAR

END_TEXT

Context("Numeric");
Context()->flags->set(
  tolerance=>0.001,
  tolType=>"absolute"
);

WEIGHTED_ANS($ans1->cmp(),40);
WEIGHTED_ANS($ans2->cmp(),60);

ENDDOCUMENT();       # This should be the last executable line in the problem.