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2,5 puntos
Parte obligatoria
Una ventana tiene forma de rectángulo y está coronada por un semicírculo. Sabiendo que el perímetro de la ventana mide 88 metros, halla las dimensiones de la ventana que permitan la mayor entrada de luz.
Ventana rectangular coronada por un semicírculo.

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FUNCIÓN DE DISTRIBUCIÓN NORMAL N(0,1)N(0,1)
Distribución normal N(0,1), con la probabilidad P(Z ≤ z) sombreada hasta z.
zz0,000,010,020,030,040,050,060,070,080,09
0,00,50000,50400,50800,51200,51600,51990,52390,52790,53190,5359
0,10,53980,54380,54780,55170,55570,55960,56360,56750,57140,5753
0,20,57930,58320,58710,59100,59480,59870,60260,60640,61030,6141
0,30,61790,62170,62550,62930,63310,63680,64060,64430,64800,6517
0,40,65540,65910,66280,66640,67000,67360,67720,68080,68440,6879
0,50,69150,69500,69850,70190,70540,70880,71230,71570,71900,7224
0,60,72570,72910,73240,73570,73890,74220,74540,74860,75170,7549
0,70,75800,76110,76420,76730,77040,77340,77640,77940,78230,7852
0,80,78810,79100,79390,79670,79950,80230,80510,80780,81060,8133
0,90,81590,81860,82120,82380,82640,82890,83150,83400,83650,8389
1,00,84130,84380,84610,84850,85080,85310,85540,85770,85990,8621
1,10,86430,86650,86860,87080,87290,87490,87700,87900,88100,8830
1,20,88490,88690,88880,89070,89250,89440,89620,89800,89970,9015
1,30,90320,90490,90660,90820,90990,91150,91310,91470,91620,9177
1,40,91920,92070,92220,92360,92510,92650,92790,92920,93060,9319
1,50,93320,93450,93570,93700,93820,93940,94060,94180,94290,9441
1,60,94520,94630,94740,94840,94950,95050,95150,95250,95350,9545
1,70,95540,95640,95730,95820,95910,95990,96080,96160,96250,9633
1,80,96410,96490,96560,96640,96710,96780,96860,96930,96990,9706
1,90,97130,97190,97260,97320,97380,97440,97500,97560,97610,9767
2,00,97720,97780,97830,97880,97930,97980,98030,98080,98120,9817
2,10,98210,98260,98300,98340,98380,98420,98460,98500,98540,9857
2,20,98610,98640,98680,98710,98750,98780,98810,98840,98870,9890
2,30,98930,98960,98980,99010,99040,99060,99090,99110,99130,9916
2,40,99180,99200,99220,99250,99270,99290,99310,99320,99340,9936
2,50,99380,99400,99410,99430,99450,99460,99480,99490,99510,9952
2,60,99530,99550,99560,99570,99590,99600,99610,99620,99630,9964
2,70,996530,996640,996740,996830,996930,997020,997110,997200,997280,99736
2,80,997440,997520,997600,997670,997740,997810,997880,997950,998010,99807
2,90,998130,998190,998250,998310,998360,998410,998460,998510,998560,99861
3,00,998650,998690,998740,998780,998820,998860,998890,998930,998960,99900
3,10,999030,999060,999100,999130,999160,999180,999210,999240,999260,99929
3,20,999310,999340,999360,999380,999400,999420,999440,999460,999480,99950
3,30,999520,999530,999550,999570,999580,999600,999610,999620,999640,99965
3,40,999660,999680,999690,999700,999710,999720,999730,999740,999750,99976
3,50,999770,999780,999780,999790,999800,999810,999810,999820,999830,99983
3,60,999840,999850,999850,999860,999860,999870,999870,999880,999880,99989
3,70,999890,999900,999900,999900,999910,999910,999920,999920,999920,99992
3,80,999930,999930,999930,999940,999940,999940,999940,999950,999950,99995
3,90,999950,999950,999960,999960,999960,999960,999960,999960,999970,99997
4,00,999970,999970,999970,999970,999970,999970,999980,999980,999980,99998
Nota: En el interior de la tabla se da la probabilidad de que la variable aleatoria ZZ, con distribución N(0,1)N(0,1), esté por debajo del valor zz.