########################################################################
## DESCRIPTION
## A WeBWorK problem  that asks students to label raw scores +/- 3
## standard deviations from the mean of a bell-shaped distribution. 
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('empirical rule', 'mean', 'standard deviation')
##
## Author('JoAnne Taormina')
## Institution('Nassau Community College')
########################################################################

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"weightedGrader.pl",
);

# make sure we're in the context we want
Context("Numeric");

#mean
$xbar = random(120, 150, 1);

#standard deviation
$stnd_dev = random(12, 30, 0.1);

$negxbar3s = $xbar-3*$stnd_dev;
$negxbar3s = Formula("$negxbar3s");
$negxbar2s= $xbar - 2*$stnd_dev;
$negxbar2s = Formula("$negxbar2s");
$negxbar1s = $xbar - $stnd_dev;
$negxbar1s = Formula("$negxbar1s");
$xbar = Formula("$xbar");
$xbar1s = $xbar + $stnd_dev;
$xbar1s = Formula("$xbar1s");
$xbar2s = $xbar + 2*$stnd_dev;
$xbar2s = Formula("$xbar2s");
$xbar3s = $xbar + 3*$stnd_dev;
$xbar3s = Formula("$xbar3s");

TEXT(beginproblem());
Context()->texStrings;
BEGIN_TEXT
Suppose a distribution is bell shaped and has the following statistics:
$BR $BR
$BCENTER
\( \bar{x}  = $xbar \)
$BR $BR
\( s = $stnd_dev \)
$ECENTER
$BR

Label the bell curve with raw scores from \( \bar{x} - 3s \) to \( \bar{x} + 3s \). Do not round any quantities. 
$BR $BR $BCENTER
\{ image( "bell_curve_image.png" , width=>450, height=>250) \}

$BR $BR
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \} $SPACE
\{ ans_rule(5) \}

$BR$BR

$ECENTER
END_TEXT

Context("Numeric");
Context()->flags->set(
  tolerance=>0.0001,
  tolType=>"absolute"
);

ANS($negxbar3s->cmp());
ANS($negxbar2s->cmp());
ANS($negxbar1s->cmp());
ANS($xbar->cmp());
ANS($xbar1s->cmp());
ANS($xbar2s->cmp());
ANS($xbar3s->cmp());

ENDDOCUMENT();