| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | September |
| Marks | 9 |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Standard +0.3 This is a standard normal distribution problem requiring use of inverse normal tables/calculator to find μ and σ from two percentile conditions, followed by a straightforward probability calculation. The setup is routine for Further Maths Statistics, involving familiar techniques (standardization, solving simultaneous equations) with no novel insight required. Slightly above average difficulty due to the algebraic manipulation needed in part (b), but well within expected FM Statistics competency. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
The heights of a population of men are normally distributed with mean $\mu$ cm and standard deviation $\sigma$ cm. It is known that 20% of the men are taller than 180 cm and 5% are shorter than 170 cm.
\begin{enumerate}[label=(\alph*)]
\item Sketch a diagram to show the distribution of heights represented by this information.
[2 marks]
\item Find the value of $\mu$ and $\sigma$.
[5 marks]
\item Three men are selected at random, find the probability that they are all taller than 175 cm.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q5 [9]}}