| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2003 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Find standard deviation from probability |
| Difficulty | Standard +0.3 This is a straightforward application of normal distribution with inverse normal calculations. Part (a) requires finding σ using P(X < 50) = 0.10 with μ = 55, part (b) is a direct probability calculation, and part (c) reverses the process. All parts use standard techniques taught in S1 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 transformation2.04g Normal distribution properties: empirical rule (68-95-99.7), points of inflection |
3. A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 50 ml of coffee. The machine actually dispenses a mean amount of 55 ml per cup and $10 \%$ of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispensed into each cup is normally distributed find
\begin{enumerate}[label=(\alph*)]
\item the standard deviation of the amount of coffee dispensed per cup in ml ,
\item the percentage of cups that contain more than 61 ml .
Following complaints, the owners of the machine make adjustments. Only $2.5 \%$ of cups now contain less than 50 ml . The standard deviation of the amount dispensed is reduced to 3 ml .
Assuming that the amount of coffee dispensed is still normally distributed,
\item find the new mean amount of coffee per cup.\\
(4)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2003 Q3 [11]}}