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Jika variabel acak X∼N(70,1 2), nilai  P(58 < X< 85) = ....

Pertanyaan

Jika variabel acak begin mathsize 14px style straight X tilde straight N left parenthesis 70 comma 1 space 2 right parenthesis end style, nilai 

begin mathsize 14px style straight P left parenthesis 58 space less than space straight X less than space 85 right parenthesis space equals space.... end style

  1. 0,1056

  2. 0,1506

     

  3. 0,5737

     

  4. 0,7357

     

  5. 0,7537

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

begin mathsize 14px style straight X tilde straight N space open parentheses 70 comma space 12 close parentheses end style 

Diperoleh begin mathsize 14px style mu equals 70 space dan space sigma equals 12 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell P open parentheses 58 less than X less than 85 close parentheses end cell equals cell P open parentheses fraction numerator 58 minus 70 over denominator 12 end fraction less than Z less than fraction numerator 85 minus 70 over denominator 12 end fraction close parentheses end cell row blank equals cell P open parentheses fraction numerator negative 12 over denominator 12 end fraction less than Z less than 15 over 12 close parentheses end cell row blank equals cell P open parentheses negative 1 less than Z less than 1 comma 25 close parentheses end cell end table end style 

Untuk menentukan hasil begin mathsize 14px style P open parentheses negative 1 less than Z less than 1 comma 25 close parentheses end style dapat dilihat nilainya pada tabel distribusi Z, sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell P open parentheses negative 1 less than Z less than 1 comma 25 close parentheses end cell equals cell P open parentheses Z less than 1 comma 25 close parentheses minus P open parentheses Z less than negative 1 close parentheses end cell row blank equals cell 0 comma 8944 minus 0 comma 1587 end cell row blank equals cell 0 comma 7357 end cell end table end style

Jadi, jawaban yang tepat adalah D.

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Pertanyaan serupa

Dengan menggunakan tabel, hitunglah probabilitas berikut. b. P(0,75<Z<2,27)

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Jawaban terverifikasi

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