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Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut. Jika variabel acak , tentukan: c.

Gunakan tabel distribusi normal Z pada lampiran untuk menyelesaikan soal berikut.

Jika variabel acak begin mathsize 14px style X tilde N space open parentheses 100 comma space 20 close parentheses end style, tentukan:

c. begin mathsize 14px style P open parentheses 120 less than X less than 167 close parentheses end style 

Jawaban:

Transformasi nilai begin mathsize 14px style X end style ke nilai begin mathsize 14px style Z end style dapat ditentukan dengan rumus berikut.

begin mathsize 14px style Z equals fraction numerator X minus mu over denominator sigma end fraction end style

Jika variabel acak begin mathsize 14px style X tilde N space open parentheses 100 comma space 20 close parentheses end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses 120 less than X less than 167 close parentheses end cell equals cell 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 equals cell P open parentheses 20 over 20 less than Z less than 67 over 20 close parentheses end cell row blank equals cell P open parentheses 1 less than Z less than 3 comma 35 close parentheses end cell row blank equals cell P open parentheses 0 less or equal than Z less or equal than 3 comma 35 close parentheses minus P open parentheses 0 less or equal than Z less or equal than 1 close parentheses end cell row blank equals cell 0 comma 4996 minus 0 comma 3413 end cell row blank equals cell 0 comma 1583 end cell end table end style

Dengan demikian, begin mathsize 14px style P open parentheses 120 less than X less than 167 close parentheses equals 0 comma 1583 end style 

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