Edexcel S1 2018 January — Question 7 11 marks

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2018
SessionJanuary
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeDirect comparison of probabilities
DifficultyStandard +0.3 This is a standard S1 normal distribution question with routine standardization and inverse normal calculations. Parts (a) and (b) are textbook exercises. Part (c) requires setting up equations with two distributions but uses straightforward algebra to find the intersection point—slightly above average difficulty due to the two-distribution setup, but still well within standard S1 scope.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation

7. The weights, \(G\), of a particular breed of gorilla are normally distributed with mean 180 kg and standard deviation 15 kg .
  1. Find the proportion of these gorillas whose weights exceed 174 kg .
  2. Find, to 1 decimal place, the value of \(k\) such that \(\mathrm { P } ( k < G < 174 ) = 0.3196\) The weights, \(B\), of a particular breed of buffalo are normally distributed with mean 216 kg and standard deviation 30 kg . Given that \(\mathrm { P } ( G > w ) = \mathrm { P } ( B < w ) = p\)
    1. find the value of \(w\)
    2. find the value of \(p\) and standard deviation 15 kg .
      1. Find the proportion of these gorillas whose weights exceed 174 kg .
      2. Find, to 1 decimal place, the value of \(k\) such that \(\mathrm { P } ( k < G < 174 ) = 0.3196\)
        Leave blankQ7

7. The weights, $G$, of a particular breed of gorilla are normally distributed with mean 180 kg and standard deviation 15 kg .
\begin{enumerate}[label=(\alph*)]
\item Find the proportion of these gorillas whose weights exceed 174 kg .
\item Find, to 1 decimal place, the value of $k$ such that $\mathrm { P } ( k < G < 174 ) = 0.3196$

The weights, $B$, of a particular breed of buffalo are normally distributed with mean 216 kg and standard deviation 30 kg .

Given that $\mathrm { P } ( G > w ) = \mathrm { P } ( B < w ) = p$
\item \begin{enumerate}[label=(\roman*)]
\item find the value of $w$
\item find the value of $p$ and standard deviation 15 kg .\\
(a) Find the proportion of these gorillas whose weights exceed 174 kg .\\
(b) Find, to 1 decimal place, the value of $k$ such that $\mathrm { P } ( k < G < 174 ) = 0.3196$

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\hfill \mbox{\textit{Edexcel S1 2018 Q7 [11]}}