Edexcel S1 — Question 7

Exam BoardEdexcel
ModuleS1 (Statistics 1)
PaperDownload PDF ↗
TopicDiscrete Probability Distributions
TypeFind cumulative distribution F(x)
DifficultyModerate -0.8 This is a standard S1 question testing basic probability distribution properties (finding parameters using E(X), stating F(x), calculating variance) and descriptive statistics from a stem-and-leaf diagram (mode, quartiles, box plot, mean, SD, skewness). All techniques are routine recall and straightforward application with no problem-solving insight required. Easier than average A-level due to being introductory statistics.
Spec5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.03e Find cdf: by integration

7. A music teacher monitored the sight-reading ability of one of her pupils over a 10 week period. At the end of each week, the pupil was given a new piece to sight-read and the teacher noted the number of errors \(y\). She also recorded the number of hours \(x\) that the pupil had practised each week. The data are shown in the table below.
  1. Given that \(\mathrm { E } ( X ) = - 0.2\), find the value of \(\alpha\) and the value of \(\beta\).
  2. Write down \(\mathrm { F } ( 0.8 )\).
    1. Evaluate \(\operatorname { Var } ( X )\).

7. A music teacher monitored the sight-reading ability of one of her pupils over a 10 week period. At the end of each week, the pupil was given a new piece to sight-read and the teacher noted the number of errors $y$. She also recorded the number of hours $x$ that the pupil had practised each week. The data are shown in the table below.
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathrm { E } ( X ) = - 0.2$, find the value of $\alpha$ and the value of $\beta$.
\item Write down $\mathrm { F } ( 0.8 )$.\\
(a) Evaluate $\operatorname { Var } ( X )$.
\end{enumerate}

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