Edexcel S1 — Question 7

Exam BoardEdexcel
ModuleS1 (Statistics 1)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBivariate data
TypeInterpret correlation coefficient value
DifficultyEasy -1.8 This is a straightforward S1 probability question involving basic conditional probability and the law of total probability. Parts (a)-(d) require simple arithmetic with given frequencies and percentages, using standard formulas. This is routine bookwork with no problem-solving insight needed, making it easier than average A-level questions.
Spec2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles

7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively. A student is chosen at random. Find the probability that this student
  1. is studying Arts subjects,
  2. does not wear glasses, given that the student is studying Arts subjects. Amongst the Science students, \(80 \%\) are right-handed. Corresponding percentages for Humanities and Arts students are 75\% and 70\% respectively. A student is again chosen at random.
  3. Find the probability that this student is right-handed.
  4. Given that this student is right-handed, find the probability that the student is studying Science subjects.
    1. (a) Describe the main features and uses of a box plot.
    Children from schools \(A\) and \(B\) took part in a fun run for charity. The times, to the nearest minute, taken by the children from school \(A\) are summarised in Figure 1. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{3d4f7bfb-b235-418a-9411-a4d0b3188254-015_398_1045_946_461}
    \end{figure}
    1. Write down the time by which \(75 \%\) of the children in school \(A\) had completed the run.
    2. State the name given to this value.
  5. Explain what you understand by the two crosses ( X ) on Figure 1.

7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively.

A student is chosen at random.

Find the probability that this student\\
(a) is studying Arts subjects,\\
(b) does not wear glasses, given that the student is studying Arts subjects.

Amongst the Science students, $80 \%$ are right-handed. Corresponding percentages for Humanities and Arts students are 75\% and 70\% respectively.

A student is again chosen at random.\\
(c) Find the probability that this student is right-handed.\\
(d) Given that this student is right-handed, find the probability that the student is studying Science subjects.\\

\begin{enumerate}
  \item (a) Describe the main features and uses of a box plot.\\

\end{enumerate}

Children from schools $A$ and $B$ took part in a fun run for charity. The times, to the nearest minute, taken by the children from school $A$ are summarised in Figure 1.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
  \includegraphics[alt={},max width=\textwidth]{3d4f7bfb-b235-418a-9411-a4d0b3188254-015_398_1045_946_461}
\end{center}
\end{figure}

(b) (i) Write down the time by which $75 \%$ of the children in school $A$ had completed the run.\\

(ii) State the name given to this value.\\

(c) Explain what you understand by the two crosses ( X ) on Figure 1.\\

\hfill \mbox{\textit{Edexcel S1  Q7}}
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