| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Interquartile range and percentiles |
| Difficulty | Moderate -0.8 This is a straightforward application of continuous uniform distribution with routine calculations. Parts (a)-(c) require basic recall of uniform distribution properties, (d) involves simple algebra to solve for s, and (e) is interpretation. All steps are standard textbook exercises with no novel problem-solving required, making it easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration5.03f Relate pdf-cdf: medians and percentiles |
A drinks machine dispenses lemonade into cups. It is electronically controlled to cut off the flow of lemonade randomly between 180 ml and 200 ml. The random variable X is the volume of lemonade dispensed into a cup.
\begin{enumerate}[label=(\alph*)]
\item Specify the probability density function of X and sketch its graph. [4]
\end{enumerate}
Find the probability that the machine dispenses
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item less than 183 ml, [3]
\item exactly 183 ml. [1]
\item Calculate the inter-quartile range of X. [3]
\item Determine the value of s such that P(X ≤ s) = 1 - 2P(X ≤ s). [2]
\item Interpret in words your value of s.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [13]}}