| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Normal distribution parameters found then approximation applied |
| Difficulty | Standard +0.3 This is a straightforward two-part question requiring (i) inverse normal calculation to find σ from a given probability, and (ii) normal approximation to binomial with continuity correction. Both are standard S2 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
3 Tennis balls are dropped from a standard height, and the height of bounce, $H \mathrm {~cm}$, is measured. $H$ is a random variable with the distribution $\mathrm { N } \left( 40 , \sigma ^ { 2 } \right)$. It is given that $\mathrm { P } ( H < 32 ) = 0.2$.\\
(i) Find the value of $\sigma$.\\
(ii) 90 tennis balls are selected at random. Use an appropriate approximation to find the probability that more than 19 have $H < 32$.
\hfill \mbox{\textit{OCR S2 2010 Q3 [9]}}