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| 1 : | jjholt | 451 | ## DESCRIPTION |
| 2 : | ## Statistics: Sampling Distributions | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## CMMK tagged this problem. | ||
| 6 : | |||
| 7 : | jj | 3229 | ## DBsubject('Statistics') |
| 8 : | ## DBchapter('Random Variables') | ||
| 9 : | ## Date('6/29/2005') | ||
| 10 : | ## Institution('UVA') | ||
| 11 : | ## Author('Cristina Murray-Krezan') | ||
| 12 : | ## TitleText1('Statistics for Management and Economics') | ||
| 13 : | ## AuthorText1('Keller, Warrack') | ||
| 14 : | ## EditionText1('6') | ||
| 15 : | ## Section1('') | ||
| 16 : | ## Problem1('') | ||
| 17 : | ## KEYWORDS('statistics', 'sampling distributions','normal sampling distributions') | ||
| 18 : | jjholt | 451 | |
| 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 : | $mu = random(110,120,1); | ||
| 37 : | $sd = random(4.7,5.7,0.1); | ||
| 38 : | $subnum = random(3,4,1); | ||
| 39 : | $a = $mu + 2; | ||
| 40 : | |||
| 41 : | BEGIN_TEXT | ||
| 42 : | $PAR | ||
| 43 : | An automatic machine in a manufacturing process is | ||
| 44 : | operating properly if the lengths of an important | ||
| 45 : | subcomponent are normally distributed with a mean | ||
| 46 : | of $mu cm and a standard deviation of $sd cm. | ||
| 47 : | $PAR | ||
| 48 : | A. Find the probability that one selected subcomponent is longer than $a cm. | ||
| 49 : | $PAR | ||
| 50 : | Probability = \{ans_rule(15)\} | ||
| 51 : | $PAR | ||
| 52 : | B. Find the probability that if $subnum subcomponents are | ||
| 53 : | randomly selected, their mean length exceeds $a cm. | ||
| 54 : | $PAR | ||
| 55 : | Probability = \{ans_rule(15)\} | ||
| 56 : | $PAR | ||
| 57 : | C. Find the probability that if $subnum are randomly selected, | ||
| 58 : | all $subnum have lengths that exceed $a cm. | ||
| 59 : | $PAR | ||
| 60 : | Probability = \{ans_rule(15)\} | ||
| 61 : | $PAR | ||
| 62 : | |||
| 63 : | END_TEXT | ||
| 64 : | #A. | ||
| 65 : | $ans1 = normal_prob($a,'infty',mean=>$mu, deviation =>$sd); | ||
| 66 : | ANS(num_cmp($ans1)); | ||
| 67 : | |||
| 68 : | #B. | ||
| 69 : | $ans2 = normal_prob($a,'infty',mean=>$mu, deviation =>$sd/sqrt($subnum)); | ||
| 70 : | ANS(num_cmp($ans2)); | ||
| 71 : | |||
| 72 : | #C. | ||
| 73 : | $ans3 = (normal_prob($a,'infty',mean=>$mu, deviation =>$sd))**$subnum; | ||
| 74 : | ANS(num_cmp($ans3)); | ||
| 75 : | |||
| 76 : | |||
| 77 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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