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Tue Jul 3 21:36:52 2007 UTC (5 years, 10 months ago) by jjholt
File size: 2808 byte(s)
```Added stat problems.  Tags to be fixed soon.
```

```    1 ## DESCRIPTION
2 ##  Statistics: Probability
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('statistics', 'probability')
6 ## naw tagged this problem.
7
8 ## DBchapter('Probability')
9 ## DBsection()
10 ## Date('6/15/2005')
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 \$a1 = random(.05,.10,.001);
37 \$a2 = random(.20,.25,.001);
38 \$a3 = random(.30,.40,.001);
39 \$a4 = random(.15,.20,.001);
40 \$a5 = 0.001*floor(1000*(1-(\$a1+\$a2+\$a3+\$a4))+.5);
41 \$c4 = ((0*\$a1)+(1*\$a2)+(2*\$a3)+(3*\$a4)+(4*\$a5));
42 \$c5 = random(20,40,1);
43 \$c6 = random(20,30,1);
44 \$c7 = (0.01*\$c6);
45 \$c8 = random(10000,20000,1000);
46 \$c9 = random(2,6,.25);
47
48
49 BEGIN_TEXT
50 \$PAR
51 To examine the effectiveness of its four annual
52 advertising promotions, a mail order company has
53 sent a questionnaire to each of its customers,
54 asking how many of the previous year's promotions
55 prompted orders that would not have otherwise
56 been made.  The accompanying table lists the
57 probabilities that were derived from the questionnaire,
58 where X is the random variable representing the number
59 of promotions that prompted orders.  If we assume
60 that overall customer behavior next year will be
61 the same as last year, what is the expected number
62 of promotions that each customer will take advantage
63 of next year by ordering goods that otherwise would
64 not be purchased?
65 \$PAR
66 \$BCENTER
67 \{begintable(6)\}
68 \{row("X", "0", "1", "2", "3", "4",)\}
69 \{row("P(X)", \$a1, \$a2, \$a3, \$a4, \$a5)\}
70 \{endtable()\}
71 \$ECENTER
72 \$PAR
73 Expected value = \{ans_rule(15)\}
74 \$PAR
75 A previous analysis of historical records found
76 that the mean value of orders for promotional
77 goods is \$c5 dollars, with the company earning
78 a gross profit of \$c6\$PERCENT on each order.
79 Calculate the expected value of the profit
80 contribution next year.
81 \$PAR
82 Expected value = \{ans_rule(15)\}
83 \$PAR
84 The fixed cost of conducting the four promotions is
85 estimated to be \$c8 dollars with a variable cost
86 of \$c9 dollars per customer for mailing and handling
87 costs.  What is the minimum number of customers required by the company
88 in order to cover the cost of promotions?  (Round your answer to the
89 next highest integer.)
90 \$PAR
91 Breakeven point = \{ans_rule(15)\}
92 \$PAR
93
94
95
96 END_TEXT
97
98
99 ANS(num_cmp(\$c4));
100 ANS(num_cmp(\$c5*\$c7*\$c4));
101 ANS(num_cmp(1 + floor(\$c8/((\$c5*\$c7*\$c4)-\$c9))));
102
103
104 ENDDOCUMENT();       # This should be the last executable line in the problem.
```