| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2023 |
| Session | January |
| Marks | 6 |
| Topic | Normal Distribution |
| Type | Symmetric probability given |
| Difficulty | Moderate -0.3 This question involves standard normal distribution calculations: (a) finding a value from a given percentage using inverse normal (z-score 1.645 for 95th percentile), and (b) using symmetry to find standard deviation from a symmetric interval about the mean. Both parts are routine applications of normal distribution properties with no conceptual challenges beyond textbook exercises. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
4.
\begin{enumerate}[label=(\alph*)]
\item The masses, in grams, of plums of a certain kind have the distribution $\mathrm { N } ( 55,18 )$. The heaviest $5 \%$ of plums are classified as extra large.
Find the minimum mass of extra large plums.
\item The masses, in grams, of apples of a certain kind have the distribution $\mathrm { N } \left( 67 , \sigma ^ { 2 } \right)$. It is given that half of the apples have masses between 62 g and 72 g .
Determine $\sigma$.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2023 Q4 [6]}}