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4Opción B

2,5 puntos
Apartado 4Bloque E

Resuelve una de las siguientes tareas (4A o 4B).

El diámetro de las mandarinas de cierta variedad se distribuye normalmente con una media de 60 mm60\,\text{mm} y una desviación típica de 16 mm16\,\text{mm}.
a
Calcula la probabilidad de que, habiendo escogido al azar una mandarina, esta tenga un diámetro menor de 40 mm40\,\text{mm} o mayor de 90 mm90\,\text{mm}.1 pt
b
Calcula la probabilidad de que, al escoger al azar dos mandarinas, ambas tengan menos de 50 mm50\,\text{mm} de diámetro.1 pt
c
Calcula la probabilidad de que, habiendo escogido al azar una mandarina, esta tenga un diámetro entre 40 mm40\,\text{mm} y 50 mm50\,\text{mm}.0,5 pts

Formulario

Mostrar
Tabla de la distribución normal N(0,1)N(0,1)P(z≤z0)=12π∫−∞z0e−z22 dz\begin{aligned}P(z \leq z_0) &= \\ &\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{z_0} e^{-\frac{z^2}{2}}\,dz\end{aligned}
Curva de la distribución normal centrada en cero, con el área acumulada sombreada hasta la abscisa positiva indicada.
z0z_00,000,010,020,030,040,050,060,070,080,09z0z_0
0,00,50000,50400,50800,51200,51600,51990,52390,52790,53190,53590,0
0,10,53980,54380,54780,55170,55570,55960,56360,56750,57140,57530,1
0,20,57930,58320,58710,59100,59480,59870,60260,60640,61030,61410,2
0,30,61790,62170,62550,62930,63310,63680,64060,64430,64800,65170,3
0,40,65540,65910,66280,66640,67000,67360,67720,68080,68440,68790,4
0,50,69150,69500,69850,70190,70540,70880,71230,71570,71900,72240,5
0,60,72570,72910,73240,73570,73890,74220,74540,74860,75170,75490,6
0,70,75800,76110,76420,76730,77040,77340,77640,77940,78230,78520,7
0,80,78810,79100,79390,79670,79950,80230,80510,80780,81060,81330,8
0,90,81590,81860,82120,82380,82640,82890,83150,83400,83650,83890,9
1,00,84130,84380,84610,84850,85080,85310,85540,85770,85990,86211,0
1,10,86430,86650,86860,87080,87290,87490,87700,87900,88100,88301,1
1,20,88490,88690,88880,89070,89250,89440,89620,89800,89970,90151,2
1,30,90320,90490,90660,90820,90990,91150,91310,91470,91620,91771,3
1,40,91920,92070,92220,92360,92510,92650,92790,92920,93060,93191,4
1,50,93320,93450,93570,93700,93820,93940,94060,94180,94290,94411,5
1,60,94520,94630,94740,94840,94950,95050,95150,95250,95350,95451,6
1,70,95540,95640,95730,95820,95910,95990,96080,96160,96250,96331,7
1,80,96410,96490,96560,96640,96710,96780,96860,96930,96990,97061,8
1,90,97130,97190,97260,97320,97380,97440,97500,97560,97610,97671,9
2,00,97720,97780,97830,97880,97930,97980,98030,98080,98120,98172,0
2,10,98210,98260,98300,98340,98380,98420,98460,98500,98540,98572,1
2,20,98610,98640,98680,98710,98750,98780,98810,98840,98870,98902,2
2,30,98930,98960,98980,99010,99040,99060,99090,99110,99130,99162,3
2,40,99180,99200,99220,99250,99270,99290,99310,99320,99340,99362,4
2,50,99380,99400,99410,99430,99450,99460,99480,99490,99510,99522,5
2,60,99530,99550,99560,99570,99590,99600,99610,99620,99630,99642,6
2,70,99650,99660,99670,99680,99690,99700,99710,99720,99730,99742,7
2,80,99740,99750,99760,99770,99770,99780,99790,99790,99800,99812,8
2,90,99810,99820,99820,99830,99840,99840,99850,99850,99860,99862,9
3,00,998650,998690,998740,998780,998820,998860,998890,998930,998960,999003,0
3,10,999030,999060,999100,999130,999160,999180,999210,999240,999260,999293,1
3,20,999310,999340,999360,999380,999400,999420,999440,999460,999480,999503,2
3,30,999520,999530,999550,999570,999580,999600,999610,999620,999640,999653,3
3,40,999660,999680,999690,999700,999710,999720,999730,999740,999750,999763,4
3,50,999770,999780,999780,999790,999800,999810,999810,999820,999830,999833,5
3,60,999840,999850,999850,999860,999860,999870,999870,999880,999880,999893,6
3,70,999890,999900,999900,999900,999910,999910,999920,999920,999920,999923,7
3,80,999930,999930,999930,999940,999940,999940,999940,999950,999950,999953,8
3,90,999950,999950,999960,999960,999960,999960,999960,999960,999970,999973,9