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Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut. Jika Variabel , tentukan: a.    b.  c.  d.  e.

Pertanyaan

Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut.
Jika Variabel X tilde N left parenthesis 100 comma 20 right parenthesis, tentukan:

a. P left parenthesis X less or equal than 96 right parenthesis  
b. P left parenthesis X greater than 134 right parenthesis
c. P left parenthesis 120 less than X less than 167 right parenthesis
d. P left parenthesis 101 less than X less or equal than 120 right parenthesis
e. P left parenthesis 117 less or equal than X less than 153 right parenthesis

Pembahasan Soal:

a. P left parenthesis X less or equal than 96 right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell less or equal than cell 96 right parenthesis equals P open parentheses Z less or equal than fraction numerator 96 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P open parentheses Z less or equal than negative 0 comma 2 close parentheses equals P left parenthesis Z less than negative 0 comma 2 right parenthesis equals 0 comma 4207 end cell end table 

b. P left parenthesis X greater than 134 right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell greater than cell 134 right parenthesis equals P open parentheses Z less than fraction numerator 134 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis Z less than 1 comma 7 right parenthesis equals 0 comma 9554 end cell row blank blank blank end table 

c. P left parenthesis 120 less than X less than 167 right parenthesis 


table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 120 end cell less than cell X less than 167 right parenthesis equals P open parentheses fraction numerator 120 minus 100 over denominator 20 end fraction less than Z less than fraction numerator 167 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell space space space space space equals P left parenthesis 1 less than Z less than 3 comma 35 right parenthesis equals P left parenthesis Z greater than 1 right parenthesis plus P left parenthesis Z less than 3 comma 35 right parenthesis equals 0 comma 8413 plus 0 comma 9996 equals 1 comma 8409 end cell end table 

d. P left parenthesis 101 less than X less or equal than 120 right parenthesis


table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 101 end cell less than cell X less or equal than 120 right parenthesis equals P open parentheses fraction numerator 101 minus 100 over denominator 20 end fraction less than Z less or equal than fraction numerator 120 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis 0 comma 05 less than Z less or equal than 1 right parenthesis equals P left parenthesis 0 comma 05 less than Z less than 1 right parenthesis equals P left parenthesis Z greater than 0 comma 05 right parenthesis plus P left parenthesis Z less than 1 right parenthesis equals 0 comma 5199 plus 0 comma 8413 equals 1 comma 3612 end cell end table

e. P left parenthesis 117 less or equal than X less than 153 right parenthesis 


table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis 117 end cell less or equal than cell X less than 153 right parenthesis equals P open parentheses fraction numerator 117 minus 100 over denominator 20 end fraction less or equal than Z less than fraction numerator 153 minus 100 over denominator 20 end fraction close parentheses end cell row blank blank cell equals P left parenthesis 0 comma 85 less or equal than Z less than 2 comma 65 right parenthesis equals P left parenthesis 0 comma 85 less than Z less than 2 comma 65 right parenthesis equals P left parenthesis Z greater than 0 comma 85 right parenthesis plus P left parenthesis Z less than 2 comma 65 right parenthesis equals 0 comma 8023 plus 0 comma 9960 equals 1 comma 7893 end cell end table

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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