Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diketahui X~N(50,64). Tentukan nilai dari x sedemikian sehingga Pr(X > x) = 0,025
- 64,65
- 65,68
- 68,76
- 76,65
- 78,76
| Diketahui | X~N(50,64) P(X > x) = 0,025 |
| Maka | \(P(X > x) = P\left( {Z > \frac{{x – \mu }}{\sigma }} \right)\)
\(P\left( {Z > \frac{{x – \mu }}{\sigma }} \right) = P\left( {Z > \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(P\left( {Z > \frac{{x – \mu }}{\sigma }} \right) = 1 – P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(0,025 = 1 – P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(0,975 = P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\({Z_{0,975}} = \frac{{x – 50}}{{\sqrt {64} }}\)
|
| Jawaban | b. 65,68 |