S2 January 2006 Q4
4. The random variable \(X \sim \mathrm{B}(150, 0.02)\).
Use a suitable approximation to estimate \(\mathrm{P}(X \gt 7)\). (4)
| Scheme | Marks |
|---|---|
| \(X = \mathrm{Po}(150 \times 0.02) = \mathrm{Po}(3)\) | B1, B1(dep) |
| \(\mathrm{P}(X \gt 7) = 1 - \mathrm{P}(X \leqslant 7)\) | M1 |
| \(= 0.0119\) | A1 |
| (4 marks) |
Notes
B1, B1(dep) po, 3
A1 awrt 0.0119
Use of normal approximation max awards B0 B0 M1 A0 in the use \(1 - \mathrm{p}(x \lt 7.5)\)
\(z = \dfrac{7.5 - 3}{\sqrt{2.94}} = 2.62\)
\(\mathrm{p}(x \gt 7) = 1 - \mathrm{p}(x \lt 7.5)\)
\(= 1 - 0.9953\)
\(= 0.0047\)