Edexcel S3 Specimen — Question 2 5 marks

Exam BoardEdexcel
ModuleS3 (Statistics 3)
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentral limit theorem
TypeState distribution of sample mean
DifficultyModerate -0.8 This is a straightforward application of the central limit theorem requiring students to state the sampling distribution of the mean (with standard error σ/√n) and then perform a routine normal probability calculation. Both parts are direct recall and standard procedure with no problem-solving or conceptual challenges.
Spec5.05a Sample mean distribution: central limit theorem

The weights of pears, \(P\) grams, are normally distributed with a mean of 110 and a standard deviation of 8. Geoff buys a bag of 16 pears.
  1. Write down the distribution of \(\overline{P}\), the mean weight of the 16 pears. [2]
  2. Find P\((110 < \overline{P} < 113)\). [3]

The weights of pears, $P$ grams, are normally distributed with a mean of 110 and a standard deviation of 8. Geoff buys a bag of 16 pears.

\begin{enumerate}[label=(\alph*)]
\item Write down the distribution of $\overline{P}$, the mean weight of the 16 pears. [2]

\item Find P$(110 < \overline{P} < 113)$. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S3  Q2 [5]}}