contoh soal Continuous probability distributions

Continuous probability distributions

1.      Data are uniformly distributed between the values of 6 and 14.

Determine the value of f (x).

            a=6 b=14

            Tentukan nilai f (x).

              f (x) =

              f (x) =1/14-6

              f (x) =

              f (x) = 0.125

What are the mean and standard deviation of this distribution?

     Apa deviasi mean dan standar distribusi ini?

µ=  

µ=  

µ=

µ = 10

σ =  

σ = 

σ =

σ = 2.3094010768

What is the probability of randomly selecting a value greater than 11?

Apa probabilitas secara acak memilih nilai lebih besar dari 11?

P(x > 11) =

P(x > 11) =3/8

P(x > 11) =0.375

 What is the probability of randomly selecting a value between 7 and 12?

   Apa probabilitas secara acak memilih nilai antara 7 dan 12?

P(7 <x< 12) =

P(7 <x< 12) = 5/8

P(7 <x< 12) =0.625

2.   Assume a normal distribution and find the following probabilities.

a.   P(x <  20 ;  m  = 25  and  s  = 4)

z =  

z =  

z= -5/4

z = -1.25

Table A.5 nilai untuk z = -1.25  adalah: 0.3944

P(x <  20) = 0,5000-0.3944

P(x <  20) =0.1056

b.   P(x  ≥ 77 ;  m  = 60 and   s  = 9)

z =

z =  

z= 17/9

z = 1.8889

Table A.5 nilai untuk z = 1,889  adalah: 0.4699

P(x  ≥ 77 )= 0.5000- 0.4699

 P(x  ≥ 77 )= 0.0301

c.   P(x  > 47 ;  m  = 50 and   s  = 8)

 z =

z =

Z = -3/8

 z = 0.375

 Table A.5 nilai untuk z =  0.375 adalah:  0.1443

                P(x  > 47) =      0,5 +      0,1443

                P(x  > 47 = 0,6443

d.   P(13  < x < 29 ; m  = 20 and   s  = 5)

 z =

z =

Z = -7/5

 z = -1.4

   

 Table A.5 nilai untuk z =  -1.4 adalah:  0.4192

   z =

z =

Z = 9/5

z = 1,8

Table A.5 nilai untuk z =  1,8 adalah: 0.4641

  P(13  < x < 29)=0.4641+  0.4192

  P(13  < x < 29)=0.8833

e.   P (x ≥ 100 ;  m  = 90 and  s = 3)

z =

z =

Z = 10/3

 z = 0.333

     Table A.5 nilai untuk z =  0.333 adalah:   0.1293

                P (x ≥ 100 ) = 0,5 -  0.1293

                P (x ≥ 100)  = 0.3707