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Tue Jul 3 21:36:52 2007 UTC (5 years, 11 months ago) by jjholt
File size: 1973 byte(s)
Added stat problems.  Tags to be fixed soon.

1 ## DESCRIPTION
2 ## Statistics: Sampling Distributions
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('statistics', 'sampling distributions','normal sampling distributions')
6 ## naw tagged this problem.
7
8 ## DBchapter('Random Variables')
9 ## DBsection()
10 ## Date('7/01/2005')
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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGnumericalmacros.pl",
28 "PGstatisticsmacros.pl",
29 "PGauxiliaryFunctions.pl"
30 );
31
32 TEXT(beginproblem());
35
36 \$n = random(10,20,1);
37 \$mu1 = random(72,77,1);
38 \$sigma1 = random(18,23,1);
39 \$mu2 = random(63,68,1);
40 \$sigma2 = random(19,24,1);
41 \$s1 = (\$sigma1)**2;
42 \$s2 = (\$sigma2)**2;
43 \$a = random(15,20,1);
44 \$b = -(\$mu1-\$mu2);
45 \$c1 = (\$s1+\$s2)**(0.5);
46 \$z1 = \$b/\$c1;
47 \$c2 = ((\$s1/5)+(\$s2/5))**(0.5);
48 \$z2 = \$b/\$c2;
49
50 BEGIN_TEXT
51 \$PAR
52 A factory's worker productivity is normally distributed.
53 One worker produces an average of \$mu1 units per day
54 with a standard deviation of \$sigma1.  Another worker
55 produces at an average rate of \$mu2 units per day with
56 a standard deviation of \$sigma2.
57 \$PAR
58 A.  What is the probability that in a single day worker
59 1 will outproduce worker 2?
60 \$PAR
61 Probability = \{ans_rule(15)\}
62 \$PAR
63 B.  What is the probability that during one week
64 (5 working days), worker 1 will outproduce worker 2?
65 \$PAR
66 Probability = \{ans_rule(15)\}
67 \$PAR
68
69 \$PAR
70
71
72 END_TEXT
73
74 \$ans1 = normal_prob(\$z1,'infty',mean=>0, deviation =>1);
75 \$ans2 = normal_prob(\$z2,'infty',mean=>0, deviation =>1);
76 ANS(num_cmp(\$ans1));
77 ANS(num_cmp(\$ans2));
78
79
80
81
82 ENDDOCUMENT();       # This should be the last executable line in the problem.