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Pertanyaan

Jika Z ∼ N ( 0 , 1 ) , maka P ( Z < − 0 , 95 ) + P ( − 0 , 33 < Z < 0 , 66 ) – P ( Z > 1 , 24 ) = ....

Jika , maka

  1. 0,6533undefined 

  2. 0,4383undefined 

  3. 0,3111undefined 

  4. 0,1797undefined 

  5. 0,0961undefined 

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S. Nur

Master Teacher

Jawaban terverifikasi

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Pembahasan

Perhatikan bahwa Kemudian dan Karena , maka perhatikan potongan tabel distribusi Normal standar berikut Dari tabel di atas, didapat bahwa Maka Kemudian dan Sehingga didapat Maka jawaban yang tepat adalah B.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses Z less than negative 0 , 95 close parentheses end cell equals cell P open parentheses Z less than 0 close parentheses minus P open parentheses negative 0 , 95 less than Z less than 0 close parentheses end cell row blank equals cell 0 , 5 minus P open parentheses 0 less than Z less than 0 , 95 close parentheses end cell end table end style

Kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses negative 0 , 33 less than Z less than 0 , 66 close parentheses end cell equals cell P open parentheses negative 0 , 33 less than Z less than 0 close parentheses plus P open parentheses 0 less than Z less than 0 , 66 close parentheses end cell row blank equals cell P open parentheses 0 less than Z less than 0 , 33 close parentheses plus P open parentheses 0 less than Z less than 0 , 66 close parentheses end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses Z greater than 1 , 24 close parentheses end cell equals cell P open parentheses Z greater than 0 close parentheses minus P open parentheses 0 less than Z less than 1 , 24 close parentheses end cell row blank equals cell 0 , 5 minus P open parentheses 0 less than Z less than 1 , 24 close parentheses end cell end table end style

Karena begin mathsize 14px style Z tilde N left parenthesis 0 comma space 1 right parenthesis end style, maka perhatikan potongan tabel distribusi Normal standar berikut

Dari tabel di atas, didapat bahwa

begin mathsize 14px style P left parenthesis 0 less than Z less than 0 comma 33 right parenthesis equals 0 comma 1293 P left parenthesis 0 less than Z less than 0 comma 66 right parenthesis equals 0 comma 2454 P left parenthesis 0 less than Z less than 0 comma 95 right parenthesis equals 0 comma 3289 P left parenthesis 0 less than Z less than 1 comma 24 right parenthesis equals 0 comma 3925 end style

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses Z less than negative 0 , 95 close parentheses end cell equals cell 0 , 5 minus P open parentheses 0 less than Z less than 0 , 95 close parentheses end cell row blank equals cell 0 , 5 minus 0 , 3289 end cell row blank equals cell 0 , 1711 end cell end table end style

Kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses negative 0 , 33 less than Z less than 0 , 66 close parentheses end cell equals cell P open parentheses 0 less than Z less than 0 , 33 close parentheses plus P open parentheses 0 less than Z less than 0 , 66 close parentheses end cell row blank equals cell 0 , 1293 plus 0 , 2454 end cell row blank equals cell 0 , 3747 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses Z greater than 1 , 24 close parentheses end cell equals cell 0 , 5 minus P open parentheses 0 less than Z less than 1 , 24 close parentheses end cell row blank equals cell 0 , 5 minus 0 , 3925 end cell row blank equals cell 0 , 1075 end cell end table end style

Sehingga didapat

begin mathsize 14px style P open parentheses Z less than negative 0 , 95 close parentheses plus P open parentheses negative 0 , 33 less than Z less than 0 , 66 close parentheses minus P open parentheses Z greater than 1 , 24 close parentheses equals 0 , 1711 plus 0 , 3747 minus 0 , 1075 equals 0 , 4383 end style

Maka jawaban yang tepat adalah B.

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