| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Find k given probability statement |
| Difficulty | Standard +0.3 This is a standard S1 normal distribution question requiring routine use of z-tables and inverse normal calculations. Part (a) is straightforward standardization, part (b) requires recognizing that P(W<k)=3P(W>k) means P(W<k)=0.75 (using P(W<k)+P(W>k)=1), part (c) tests vocabulary (median), and part (d) reverses the process using percentiles. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(W>92)=P\!\left(Z>\frac{92-99}{3.6}\right)=P(Z>-1.94)\) or \(P(Z<1.94)=0.9738\) | M1, A1, A1 | M1 for standardising with 92, 99, 3.6; 1st A1 for correct probability statement and \(z\approx\pm1.94\); 2nd A1 for awrt 0.974 |
| Answer | Marks | Guidance |
|---|---|---|
\(P(W| B1, M1 B1, A1cao |
1st B1 for \(P(W |
|
| Answer | Marks | Guidance |
|---|---|---|
| \(k\) is the upper quartile | B1 | Allow \(Q_3\), third quartile, or 75th percentile |
| Answer | Marks | Guidance |
|---|---|---|
\(P(W| M1 B1, A1 |
M1 standardising set equal to \(z\) in \(0.8\)–\(0.9\); B1 for \(\pm0.8416\); A1 for awrt 4.75 |
|
# Question 7:
## Part (a)
| $P(W>92)=P\!\left(Z>\frac{92-99}{3.6}\right)=P(Z>-1.94)$ or $P(Z<1.94)=0.9738$ | M1, A1, A1 | M1 for standardising with 92, 99, 3.6; 1st A1 for correct probability statement and $z\approx\pm1.94$; 2nd A1 for awrt 0.974 |
## Part (b)
| $P(W<k)=3P(W>k)$, so $P(W<k)=0.75$; $\frac{k-99}{3.6}=0.67$; $k=101.4$ | B1, M1 B1, A1cao | 1st B1 for $P(W<k)=0.75$ or $P(W>k)=0.25$; M1 standardising with $k$, 99, 3.6; 2nd B1 for $\pm0.67$; A1 for 101.4 (1dp) |
## Part (c)
| $k$ is the upper quartile | B1 | Allow $Q_3$, third quartile, or 75th percentile |
## Part (d)
| $P(W<P_{20})=0.2$; $\frac{116-120}{\sigma}=-0.8416$; $\sigma=4.7528\ldots$ | M1 B1, A1 | M1 standardising set equal to $z$ in $0.8$–$0.9$; B1 for $\pm0.8416$; A1 for awrt 4.75 |
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Could you please share the actual pages containing the mark scheme questions and answers? This appears to be either a blank page or the final/back cover of the document.\begin{enumerate}
\item The birth weights, $W$ grams, of a particular breed of kitten are assumed to be normally distributed with mean 99 g and standard deviation 3.6 g\\
(a) Find $\mathrm { P } ( W > 92 )$\\
(b) Find, to one decimal place, the value of $k$ such that $\mathrm { P } ( W < k ) = 3 \mathrm { P } ( W > k )$\\
(c) Write down the name given to the value of $k$.
\end{enumerate}
For a different breed of kitten, the birth weights are assumed to be normally distributed with mean 120 g
Given that the 20th percentile for this breed of kitten is 116 g\\
(d) find the standard deviation of the birth weight of this breed of kitten.\\
\hfill \mbox{\textit{Edexcel S1 2015 Q7 [11]}}