| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2013 |
| Session | November |
| Marks | 9 |
| Topic | Normal Distribution |
| Type | Mixed calculations with boundaries |
| Difficulty | Moderate -0.3 This is a straightforward application of normal distribution with standard z-score calculations and inverse normal lookups. All three parts follow routine procedures (finding P(X<300), solving for μ when P(X<300)=0.05, solving for σ when P(X<300)=0.05) with no conceptual challenges beyond basic statistical interpretation. The final explanation requires minimal economic reasoning. Slightly easier than average due to its procedural nature, though the multi-part structure and context provide some substance. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
A company supplies tubs of coleslaw to a large supermarket chain. According to the labels on the tubs, each tub contains 300 grams of coleslaw. In practice the weights of coleslaw in the tubs are normally distributed with mean 305 grams and standard deviation 6 grams.
\begin{enumerate}[label=(\roman*)]
\item Find the proportion of tubs that are underweight, according to the label. [3]
\end{enumerate}
The supermarket chain requires that the proportion of underweight tubs should be reduced to 5%.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item If the standard deviation is kept at 6 grams, find the new mean weight needed to achieve the required reduction. [3]
\item If the mean weight is kept at 305 grams, find the new standard deviation needed to achieve the required reduction. Explain why the company might prefer to adjust the standard deviation rather than the mean. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2013 Q6 [9]}}