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Umur suatu merek aki berdistribusi normal dengan s...

Umur suatu merek aki berdistribusi normal dengan simpangan baku begin mathsize 14px style 0 comma 6 end style tahun. Jika sebanyak begin mathsize 14px style 1 comma 22 percent sign end style aki mencapai umur kurang dari begin mathsize 14px style 2 comma 8 end style tahun, berapa rata-rata umur aki?

Jawaban:

Dari soal dapat diketahui:

begin mathsize 14px style delta equals 0 comma 6 end style dan begin mathsize 14px style straight P open parentheses straight X less or equal than 2 comma 8 close parentheses equals 1 comma 22 percent sign equals 0 comma 0122 space rightwards arrow space straight Z equals negative 2 comma 25 end style 

Maka:

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space straight Z equals fraction numerator straight X minus straight mu over denominator straight delta end fraction space space space space space space space space space space space minus 2 comma 25 equals fraction numerator 2 comma 8 minus straight mu over denominator 0 comma 6 end fraction space open parentheses negative 2 comma 25 close parentheses open parentheses 0 comma 6 close parentheses equals 2 comma 8 minus straight mu space space space space space space space space space space space minus 1 comma 35 equals 2 comma 8 minus straight mu space space space space space space space space space space space space space space space space space space space straight mu equals 2 comma 8 plus 1 comma 35 space space space space space space space space space space space space space space space space space space space straight mu equals 4 comma 15 end style  

Jadi, rata-rata umur aki adalah begin mathsize 14px style 4 comma 15 end style tahun.

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