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Jika variabel acak  dan nilai , nilai  adalah ....

Pertanyaan

Jika variabel acak begin mathsize 14px style straight X tilde straight N open parentheses 90 comma space straight sigma close parentheses end style dan nilai begin mathsize 14px style straight P open parentheses straight X greater than 61 close parentheses equals 87 comma 7 percent sign end style, nilai begin mathsize 14px style straight sigma end style adalah .... 

  1. 22 begin mathsize 14px style space space space end style 

  2. 23   begin mathsize 14px style space space space end style 

  3. 25   begin mathsize 14px style space space space end style 

  4. 28   begin mathsize 14px style space space space end style 

  5. 29   begin mathsize 14px style space space space end style 

Pembahasan Soal:

Diketahui variabel acak begin mathsize 14px style straight X tilde straight N open parentheses 90 comma space straight sigma close parentheses end style, sehingga begin mathsize 14px style straight mu equals 90 end style, dan nilai begin mathsize 14px style straight P open parentheses straight X greater than 61 close parentheses equals 87 comma 7 percent sign end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight P open parentheses straight X greater than 61 close parentheses equals straight P open parentheses straight Z greater than fraction numerator 61 minus straight mu over denominator straight sigma end fraction close parentheses end cell equals cell 1 minus straight P open parentheses straight Z less than fraction numerator 61 minus straight mu over denominator straight sigma end fraction close parentheses end cell row cell 87 comma 7 percent sign end cell equals cell 1 minus straight P open parentheses straight Z less than fraction numerator 61 minus 90 over denominator straight sigma end fraction close parentheses end cell row cell straight P open parentheses straight Z less than fraction numerator 61 minus 90 over denominator straight sigma end fraction close parentheses end cell equals cell 1 minus 87 comma 7 percent sign end cell row cell straight P open parentheses straight Z less than fraction numerator negative 29 over denominator straight sigma end fraction close parentheses end cell equals cell 1 minus 0 comma 877 end cell row cell straight P open parentheses straight Z less than fraction numerator negative 29 over denominator straight sigma end fraction close parentheses end cell equals cell 0 comma 123 end cell end table end style 

Sehingga diperoleh begin mathsize 14px style z equals fraction numerator negative 29 over denominator straight sigma end fraction end style.

Untuk menentukan nilai begin mathsize 14px style straight sigma end style harus dicari terlebih dahulu nilai begin mathsize 14px style z end style. Nilai begin mathsize 14px style z end style dapat diperoleh dari tabel distribusi begin mathsize 14px style z end style dengan cara mencocokkan atau mencari letak begin mathsize 14px style 0 comma 123 end style sehingga diperoleh nilai begin mathsize 14px style z equals negative 1 comma 16 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row z equals cell fraction numerator negative 29 over denominator straight sigma end fraction end cell row cell negative 1 comma 16 end cell equals cell fraction numerator negative 29 over denominator straight sigma end fraction end cell row straight sigma equals cell fraction numerator negative 29 over denominator negative 1 comma 16 end fraction end cell row straight sigma equals 25 end table end style 

Jadi jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Februari 2021

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