Edexcel S2 — Question 4 11 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks11
PaperDownload PDF ↗
TopicContinuous Uniform Random Variables
TypeCumulative distribution function
DifficultyModerate -0.8 This is a straightforward application of continuous uniform distribution with standard bookwork questions: identifying the model, calculating mean using the formula (a+b)/2, writing down the CDF, and finding a simple probability. All parts require direct recall of formulas with minimal problem-solving, making it easier than average but not trivial due to the multi-part structure and need to correctly interpret the context.
Spec5.02e Discrete uniform distribution5.03e Find cdf: by integration

Jean catches a bus to work every morning. According to the timetable the bus is due at 8 a.m., but Jean knows that the bus can arrive at a random time between five minutes early and 9 minutes late. The random variable X represents the time, in minutes, after 7.55 a.m. when the bus arrives.
  1. Suggest a suitable model for the distribution of X and specify it fully. [2]
  2. Calculate the mean time of arrival of the bus. [3]
  3. Find the cumulative distribution function of X. [4]
Jean will be late for work if the bus arrives after 8.05 a.m.
  1. Find the probability that Jean is late for work. [2]

Jean catches a bus to work every morning. According to the timetable the bus is due at 8 a.m., but Jean knows that the bus can arrive at a random time between five minutes early and 9 minutes late. The random variable X represents the time, in minutes, after 7.55 a.m. when the bus arrives.

\begin{enumerate}[label=(\alph*)]
\item Suggest a suitable model for the distribution of X and specify it fully. [2]
\item Calculate the mean time of arrival of the bus. [3]
\item Find the cumulative distribution function of X. [4]
\end{enumerate}

Jean will be late for work if the bus arrives after 8.05 a.m.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the probability that Jean is late for work. [2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2  Q4 [11]}}