########################################################################
## DESCRIPTION
## A WeBWorK problem that asks students to find the area under the normal curve
## based on given z-scores.
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('normal curve', 'area', 'z-score')
##
## 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",
"PGnauGraphics.pl",
);

install_weighted_grader();

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

$a = random(-2.3,-.01,.01);
$b = random(0,2.3,.01);
$c = random(-2.3,-.01,.01);
$d = random(0,2.3,.01);
$e = random(0,2.3,.01);
$f = random(-2.3,-.01,.01);
$g = random(-2.3,-.01,.01);
$h = random(0,2.3,.01);

$diagram1 = DrawNormalDist( $a, $b, $a, $b);
$ans1 = normal_prob($a, $b);
# round $ans1 to 4 decimal places
$ans1 = int(10000*$ans1+.5*($ans1 <=> 0))/10000;

$diagram2 = DrawNormalDist( $c, $d, $c, $d);
$ans2 = normal_prob($c, $d);
# round $ans2 to 4 decimal places
$ans2 = int(10000*$ans2+.5*($ans2 <=> 0))/10000;

$diagram3 = DrawNormalDist( -INF, $e, "", $e);
$ans3 = normal_prob(-"infty", $e);
# round $ans3 to 4 decimal places
$ans3 = int(10000*$ans3+.5*($ans3 <=> 0))/10000;

$diagram4 = DrawNormalDist( -INF, $f, "", $f);
$ans4 = normal_prob(-"infty", $f);
# round $ans4 to 4 decimal places
$ans4 = int(10000*$ans4+.5*($ans4 <=> 0))/10000;

$diagram5 = DrawNormalDist( $g, INF, $g, "");
$ans5 = normal_prob($g, "infty");
# round $ans5 to 4 decimal places
$ans5 = int(10000*$ans5+.5*($ans1 <=> 0))/10000;

$diagram6 = DrawNormalDist( $h, INF, $h, "");
$ans6 = normal_prob($h, "infty");
# round $ans6 to 4 decimal places
$ans6 = int(10000*$ans6+.5*($ans6 <=> 0))/10000;

$ans1 = Compute($ans1);
$ans2 = Compute($ans2);
$ans3 = Compute($ans3);
$ans4 = Compute($ans4);
$ans5 = Compute($ans5);
$ans6 = Compute($ans6);

BEGIN_TEXT
$BCENTER
\{Plot($diagram1, tex_size=>900);\}
$ECENTER $BR
(a) Find the area under the normal curve between z= $a and z= $b. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram2, tex_size=>900);\}
$ECENTER $BR
(b) Find the area under the normal curve between z= $c and z= $d. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram3, tex_size=>900);\}
$ECENTER $BR
(c) Find the area under the normal curve that lies to the left of z= $e. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR 
answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram4, tex_size=>900);\}
$ECENTER $BR
(d) Find the area under the normal curve that lies to the left of z= $f. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR 
answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram5, tex_size=>900);\}
$ECENTER $BR
(e) Find the area under the normal curve that lies to the right of z= $g. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR
answer: \{ans_rule(10)\} $PAR $HR
$BCENTER
\{Plot($diagram6, tex_size=>900);\}
$ECENTER $BR
(f) Find the area under the normal curve that lies to the right of z= $h. $BITALIC Express your answer as a decimal. Round to 4 decimal places after the decimal point.$EITALIC $BR
answer: \{ans_rule(10)\} $PAR $HR

END_TEXT

Context("Numeric");
Context()->flags->set(
  tolerance=>0.00001,
  tolType=>"absolute"
);

WEIGHTED_ANS($ans1->cmp(),14);
WEIGHTED_ANS($ans2->cmp(),14);
WEIGHTED_ANS($ans3->cmp(),18);
WEIGHTED_ANS($ans4->cmp(),18);
WEIGHTED_ANS($ans5->cmp(),18);
WEIGHTED_ANS($ans6->cmp(),18);

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