| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2018 |
| Session | June |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Compare approximation methods |
| Difficulty | Moderate -0.3 This question tests standard application of normal and Poisson approximations to binomial distributions with appropriate continuity corrections. Part (i) is routine (np=40, npq=32, use normal), part (ii) is also standard (np=4, p small, use Poisson). Both require only recall of approximation conditions and direct calculation with no problem-solving insight, making it slightly easier than average. |
| Spec | 2.04d Normal approximation to binomial5.02d Binomial: mean np and variance np(1-p)5.02n Sum of Poisson variables: is Poisson |
1 (i) The random variable $X$ has the distribution $\mathrm { B } ( 200,0.2 )$. Use a suitable approximation to find $\mathrm { P } ( X \leqslant 30 )$.\\
(ii) The random variable $Y$ has the distribution $\mathrm { B } ( 200,0.02 )$. Use a suitable approximation to find $\mathrm { P } ( Y \leqslant 3 )$.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2018 Q1}}