Tarea de Calidad

Ingenier\u00eda de Calidad Cueto Vargas Jonathan Alfredo 05210771 1.-Dado los siguientes datos encontrar a y b. Z = (X - \u00b5)/\u03c3 X \u2248 N (5,9)

Z = (X - \u00b5)/\u03c3 P(a \u2264 x \u2265 b) = 80%

-1.28 = (X1 \u2013 5)/3

Z = (X - \u00b5)/\u03c3

-3.84 = X1 \u2013 5

\u00b5=5

\u03c32 = 9

1.28 = (X1 \u2013 5)/3 3.84 = X1 \u2013 5

1.16 = X1 = a

8.84 = X1 = b

80%

10%

90%

-1.28

1.28

2.-Si un conjunto de observaciones est\u00e1 distribuido normalmente, que porcentaje de ellos difiere de la media por a) m\u00e1s 1.3 \u03c3, b) menos 0.52 \u03c3. a) 1- P(1.3) = 2X = 1 \u2013 0.9032 = 2(0.0968) = 0.1936 = 19.36% P (\u0399 X - \u00b5 \u0399 > 1.3) b) 1 \u2013 P(0.52) = 2X = 1 \u2013 0.6985 = 2(0.3015) = 0.603 1 \u2013 0.603 = 0.397 = 39.7%

-1.3

1.3

0.0968

0.9032

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3.-Cierto proceso de manufactura produce termos de un di\u00e1metro de 1.2 y 1.25,

Z = (X - \u00b5)/\u03c3 = (1.25 \u2013 1.21)/0.02 = 2

1.2

1.21

1.25

33.13%

4.-Un eje consiste en seis secciones diferentes colocadas una al lado de la otra.

(8.1, 0.05); (7.25, 0.04); (9.75, 0.06); (3.45, 0.04); (17.15, 0.10); (6.20, 0.07) Si las especificaciones establecen que el eje ensamblado tenga una longitud de

\u00b5y = \u00b51 + \u00b52 + \u00b53 +\u2026

\u03c32y = \u03c321 + \u03c322 + \u03c323 +\u2026 \u00b5y = 8.1+7.25+9.75+3.45+17.15+6.2 = 51.9

\u03c32y = 0.05+0.04+0.06+0.04+0.1+0.07 = 0.36 Z = (X - \u00b5)/\u03c3 = (53.5 \u2013 51.9)/0.6 = 2.66

50.5

51.9

53.8

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5.-Una maquina de sodas est\u00e1 regulada de tal manera que su descarga tiene

\u00b5x \u00b1 2\u03c3x

-2 \u03c3

t = (X - \u00b5)/ (\u03c3/\u221an) = (219 \u2013 207)/ (15/\u22 12/5 =2.4 \u201cSe debe ajustar\u201d

2\u03c3

6.-La vida promedio de cierto motor peque\u00f1o es de 10 a\u00f1os con una desviaci\u00f3n

0.03 X

Z = (X - \u00b5)/\u03c3

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7.-Para una distribución t con 15gl hallar el valor t dado que: a) El área a la

a) t = 2.602

8.-El fabricante de una patente médica sostiene que la misma tiene un 90% de

0.9 1.28 N = 200

H0: P = 90%

-20/√18 = -20/4.2426 = -4.7114 Zα/2 = -1.96 Z

*

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9.-Un fabricante de fusibles dice que su producto se funde con una intensidad

a)

µ = 15 b)

α

=

5 %

Error en decisión Tipo Rechazar H0 verdadera I Aceptar H0 falsa II

α = 5% β = 95% α = 1% β = 99%

Probabilidad α β