6.- P (B∩F)= 15/50

P(B)= 25/50

P(F)=20/50

a) P(FUB)= P(F)+ P(B)- P (B∩F)= 20/50+ 25/50 -15/50= 0.6

b) P(F/B)= P (F∩B)P(B)

= 15/5025/50

= 0.6

c) 1-0.6= 0.4

7.- a) P(O)= 44/100 =O.44

b) P (Rh-) =15/100= 0.15

d) P (RH-) x P (RH-) = (0.05) x (0.05) = 0.025

e) P (RH-) x P (RH-) = (0.015) x (0.015) = 0.0225

f) P (RH-/ O) =P (RH−∩O)

P(O) = 0.60.44

= 0.14

g) P (B/ RH-) = P ¿¿= 0.90.85

= 0.11

8.- μ =8.2 P(X<7)

σ =1.1 P(X−μσ

< 7−8.21.1

)

P (Z< -1.09) =0.1378

9.- μ =268 P(X< 247)= P(X−μσ

< 247−26815

σ =1.1 =P (Z< -1.4) =0.8076En porcentaje: 0.8076 x100%= 8.076

10.- a) P(X>131.5)

P(X−μσ

< 131.5−100

15)

P(z>2.1)= 1- P(z<2.1) = 0.01786

b) n= 75000 p=0.01786E(x)=np

E(x)= 75000 x 0.01786 =1339.5

11.- μ =1.725 P(X−μσ

< x<X−μσ

)

σ =0.07 p( 1.60−1.7250.07

< z<1.95−1.725

0.07 )

P(-1.79 <z< 3.21)= P(z<3.21) - P(z<-1.79)= 0.96261

12.- μ =178.1 P(X< X) = 0.07

σ =40.7 P(Z>X−178.140.7

) =0.07

1- P(Z< X−178.140.7

) = 0.07

P(Z< X−178.140.7

) =0.93

Z= 1.48

X−178.140.7

= 148

X=238.336

13.- A. 50/200= 0.25

B. 40/200= 0.2

C. 150/200= 0.75

EJERCICIOS

a) P (Z< 1.25) =0.89435

b) P (Z< -2.28)= 0.01130

c) P (Z< 0) =0.50000

d) P (0<Z< 2.5) = P (Z< 2.5)- P (Z<0)

= 0.99702-0.50000

=0.49702

e) P (-2.38 <Z< 0)= P (Z< 0)- P (Z<-2.38)

=0.50000- 0.00866

=0.49134

f) P (-2.25<Z< 2.25)= P (Z< 2.25)- P (Z<-2.38)

= 0.98778-0.01222

=0.97556

h)P (1.55<Z< 2.35)= P (Z< 2.35)- P (Z<1.55)

= 0.99061-0.93943 = 0.05118

i) P (Z>1.43) =1- P (Z< 2.43)

=1-0.99245

=0.00755

2.- μ =1.725 P(20<X<35)

σ 2 =25 P( 20−305

< z<35−305

)

σ =5 P(-2<Z<1)= P (Z<1) - P (Z< 2)

= 0.84134- 0.97725

= -0.13591

3.- μ =60 P(55<X<65)

σ =3 P( 55−603

< z<65−603

)

P(-1.67<Z<1.67)= P (Z<1.67) - P (Z< -1.67)

=

4.- μ =64.3 1- 2[ P(X<Z<64.3-b)= 0.683

σ =2.3 P(X<Z<64.3-b)= 0.1585

P(Z< -b/2.3)=0.1585 64.3-b 64.3+b

Z=-1=-b/2.3

b=2.3

62 0 66.5

5.- μ =16 P(X>16)

σ 2 =4 P(Z>0)

σ =2 1-P(Z<0) =1-0.5 =0.5