Estadistica

Ejercicio 33 Capitulo 5

a) f(x)=(n¦x) p^x 〖(1-p)〗^((n-x))

(n¦x)=n!/x!(n-x)! = 20!/12!(20-12)! = 125,970

p^x 〖(1-p)〗^((n-x))= 〖0.5〗^12 〖(1-0.5)〗^((20-12))= (0.000244140625)(0.00390625)= 0.000000953674316

f(x)= (125,970)( 0.000000953674316) = 0.120134 = 12.01%

b) 2.06%

c) E(x)=μ=np = (20)(0.5) = 10

d) Var(x)=σ^2=np(1-p) = (20)(0.5) (1 - 0.5) = 5

σ= √5 = 2.23

Ejercicio 51 Capitulo 5

a) 2.19% b) 21.97%

c) 49.45% d) 26.37%

Ejercicio 47 capítulo 6

Z =(Xi-media)/σ = (100,000-88,592)/19,900 = 0.5732

P(z) = 0.7157

1 – P(z) = 1 – 0.7157 = 0.2843 = 28.43%

Z =(Xi-media)/σ = (100,000-97,417)/21,800 = 0.1184

P(z) = 0.5438

1 – P(z) = 1 – 0.5438 = 0.4562 = 45.62%

Z =(Xi-media)/σ = (75,000-97,417)/21,800 = -1.02

P(z) = 0.1539 = 15.39%

Z =(Xi-media)/σ = (Xi-88,592)/19,900 = 2.33

Xi = Z σ + Media = (2.33)(19,900) + 88,592 = $134,959

Ejercicio 53 capítulo 6

f(x)= 1/μ^(e^(-x/μ) ) = 1/〖38.3〗^(e^(-x/38.3) )

P(x ≤x_0)=1- e^(-x_(0/) μ)

P(x ≤x_0)=1- e^(-40/38.3) = 0.6480

P(x ≤x_0)=1- e^(-20/38.3 )= 0.4067

P(x ≤x_0)=0.6480- 0.4067 = 0.2413 = 24.13%

P(x ≤x_0)=1- e^(-x_(0/) μ)

P(x ≤x_0)=1- e^(-60/38.3) = 0.7912

P(x >60)=1-(P≤60) = 1 – 0.7912 = 0.2088 = 20.88%

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