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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) = ....

  1. 0,6533

  2. 0,4383

  3. 0,3111

  4. 0,1797

  5. 0,0961

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

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 Z~N(0, 1), maka perhatikan potongan tabel distribusi Normal standar berikut

Dari tabel di atas, didapat bahwa

P(0 < Z < 0,33) = 0,1293

P(0 < Z < 0,66) = 0,2454

P(0 < Z < 0,95) = 0,3289

P(0 < Z < 1,24) = 0,3925

 

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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