Merge pull request #1154 from gajennings/main

Fix bug 4827, update to MathObjects and PGML, add solution

Author: gajennings

OpenProblemLibrary/ASU-topics/setStat/dueck7_3_4.pg

@@ -16,37 +16,41 @@ DOCUMENT();
 
 loadMacros(
   "PGstandard.pl",
-  "PGchoicemacros.pl",
-  "PGgraphmacros.pl",
-  "PGnumericalmacros.pl",
+  "MathObjects.pl",
+  "PGML.pl",
   "PGstatisticsmacros.pl",
   "PGcourse.pl"
 );
 
-TEXT(beginproblem());
 $showPartialCorrectAnswers = 1;
 
+Context("Numeric");
+
 $n = random(5,10,1);
 $mean = random(12.09,12.15,0.01);
 $dev = random(0.09,0.13,0.01);
 $newdev = $dev/sqrt($n);
-$ans = normal_prob($mean, 'infty', mean=>12, deviation=>$newdev);
-
-BEGIN_TEXT
+$z = Compute( "($mean - 12)/$newdev" );
+$p = normal_prob($mean, 'infty', mean=>12, deviation=>$newdev);
+$ans = Compute($p)->cmp(
+  tolerance => 0.005,
+  tolType => 'relative'
+);
 
-Cans of regular Coke are labeled as containing \(12 \mbox{ oz}\). $BR
-Statistics students weighed the contents of \($n\) randomly chosen cans, and found the mean
-weight to be \($mean\) ounces. $BR
+BEGIN_PGML
 
-Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of \(12.00 \mbox{ oz}\)
-and a standard deviation of \($dev \mbox{ oz}\). Find the probability that a sample of \($n\) cans will 
-have a mean amount of at least \($mean \mbox{ oz}\). $BR
+Cans of regular Coke are labeled as containing [`12 \text{ oz}`].    
+Statistics students weighed the contents of [$n] randomly chosen cans, and found the mean
+weight to be [$mean] ounces.     
 
-\{ans_rule(10)\}
+Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of [$dev] oz. Find the probability that a sample of [$n] cans will have a mean amount of at least [$mean]  oz. 
 
-END_TEXT
+[_______]{$ans}
 
-ANS(num_cmp($ans,tol=>0.0005));
+END_PGML
 
+BEGIN_PGML_SOLUTION
+The z-score is [`z = \frac{x-\mu}{\sigma/\sqrt{n}} = \frac{[$mean]-12.00}{[$dev]/\sqrt{[$n]}} = [$z]`].  Using a computer or a table one finds that the probability [`z > [$z]`] is [$p] (approximately). 
+END_PGML_SOLUTION
 ENDDOCUMENT();       # This should be the last executable line in the problem.