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| 1 : | jjholt | 451 | ## DESCRIPTION |
| 2 : | ## Statistics: Probability | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('statistics', 'probability') | ||
| 6 : | ## naw tagged this problem. | ||
| 7 : | |||
| 8 : | ## DBchapter('Continuous Probability Distributions') | ||
| 9 : | ## DBsection() | ||
| 10 : | ## Date('6/28/2005') | ||
| 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 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGnumericalmacros.pl", | ||
| 28 : | "PGstatisticsmacros.pl", | ||
| 29 : | "PGauxiliaryFunctions.pl" | ||
| 30 : | ); | ||
| 31 : | |||
| 32 : | TEXT(beginproblem()); | ||
| 33 : | $showPartialCorrectAnswers = 1; | ||
| 34 : | ## install_problem_grader(~~&std_problem_grader); | ||
| 35 : | |||
| 36 : | $z = 4; | ||
| 37 : | |||
| 38 : | while ($z > 3) { | ||
| 39 : | $a = random(60000,70000,10000); | ||
| 40 : | $b = $a+random(10000,15000,1000); | ||
| 41 : | $c = random(3000,7000,1000); | ||
| 42 : | $d = $b+random(3000,10000,1000); | ||
| 43 : | $z = ($b-$a)/$c; | ||
| 44 : | } | ||
| 45 : | |||
| 46 : | BEGIN_TEXT | ||
| 47 : | $PAR | ||
| 48 : | The top-selling Red and Voss tire is rated $a miles, which means nothing. | ||
| 49 : | In fact, the distance the tires can run until wear-out is a normally distributed random | ||
| 50 : | variable with a mean of $b miles and a standard deviation of $c miles. | ||
| 51 : | $PAR | ||
| 52 : | A. What is the probability that the tire wears out before $a miles? | ||
| 53 : | $PAR | ||
| 54 : | Probability = \{ans_rule(15)\} | ||
| 55 : | $PAR | ||
| 56 : | B. What is the probability that a tire lasts more than $d miles? | ||
| 57 : | $PAR | ||
| 58 : | Probability = \{ans_rule(15)\} | ||
| 59 : | $PAR | ||
| 60 : | |||
| 61 : | |||
| 62 : | |||
| 63 : | |||
| 64 : | END_TEXT | ||
| 65 : | |||
| 66 : | $ans1 = normal_prob('-infty', $a, mean=>$b, deviation=>$c); | ||
| 67 : | $ans2 = normal_prob($d, 'infty', mean=>$b, deviation=>$c); | ||
| 68 : | ANS(num_cmp($ans1)); | ||
| 69 : | ANS(num_cmp($ans2)); | ||
| 70 : | |||
| 71 : | |||
| 72 : | |||
| 73 : | |||
| 74 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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