| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 8 |
| Topic | Normal Distribution |
| Type | Linear relationship μ = kσ |
| Difficulty | Standard +0.3 This is a standard normal distribution question requiring routine z-score calculations and inverse normal lookups. Parts (i)(a-c) are textbook exercises with straightforward standardization. Part (ii) adds mild complexity by requiring algebraic manipulation to standardize when σ depends on μ, but this is still a common exam pattern. Slightly above average due to the multi-part nature and part (ii)'s algebraic twist, but no novel problem-solving required. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
2.\\
(i) The variable $X$ has the distribution $\mathrm { N } ( 20,9 )$.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { P } ( X > 25 )$.
\item Given that $\mathrm { P } ( X > a ) = 0.2$, find $a$.
\item Find $b$ such that $\mathrm { P } ( 20 - b < X < 20 + b ) = 0.5$.\\
(ii) The variable $Y$ has the distribution $\mathrm { N } \left( \mu , \frac { \mu ^ { 2 } } { 9 } \right)$. Find $\mathrm { P } ( Y > 1.5 \mu )$.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q2 [8]}}