Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Probabilitas dan Statistika |
| Periode Ujian |
: |
November 2018 |
| Nomor Soal |
: |
25 |
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 |
\(P(X > x) = P\left( {Z > \frac{{x – \mu }}{\sigma }} \right)\)
\(P\left( {Z > \frac{{x – \mu }}{\sigma }} \right) = P\left( {Z > \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(P\left( {Z > \frac{{x – \mu }}{\sigma }} \right) = 1 – P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(0,025 = 1 – P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\(0,975 = P\left( {Z < \frac{{x – 50}}{{\sqrt {64} }}} \right)\)
\({Z_{0,975}} = \frac{{x – 50}}{{\sqrt {64} }}\)
- Pada table Distribusi Normal, \({Z_{0,975}} = 1,96\)
\(1,96 = \frac{{x – 50}}{{\sqrt {64} }}\)
\(x = 65,68\) |
| Jawaban |
b. 65,68 |
