CAIE S1 2014 June — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeInterval probability P(a < X < b)
DifficultyModerate -0.8 This is a straightforward normal distribution probability calculation requiring standardization of two values and looking up z-scores in tables. It's a direct application of the standard procedure with no complications, making it easier than average but not trivial since it requires correct execution of multiple steps.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
1 The petrol consumption of a certain type of car has a normal distribution with mean 24 kilometres per litre and standard deviation 4.7 kilometres per litre. Find the probability that the petrol consumption of a randomly chosen car of this type is between 21.6 kilometres per litre and 28.7 kilometres per litre.
\(P(21.6 < x < 28.7)\)
AnswerMarks Guidance
\(= P\left(\frac{21.6-24}{4.7} < z < \frac{28.7-24}{4.7}\right)\)M1 Standardising; no cc, no sq rt
\(= P(-0.5106 < z < 1)\)M1 \(\Phi_1 + \Phi_2 - 1\)
\(= \Phi(1) - \Phi(-0.5106)\)
\(= 0.8413 - (1 - 0.6953)\)
\(= 0.537\) (0.5366)A1 4 
$P(21.6 < x < 28.7)$

$= P\left(\frac{21.6-24}{4.7} < z < \frac{28.7-24}{4.7}\right)$ | M1 | Standardising; no cc, no sq rt
$= P(-0.5106 < z < 1)$ | M1 | $\Phi_1 + \Phi_2 - 1$
$= \Phi(1) - \Phi(-0.5106)$ | | 
$= 0.8413 - (1 - 0.6953)$ | | 
$= 0.537$ (0.5366) | A1 | 4 | Correct answer
1 The petrol consumption of a certain type of car has a normal distribution with mean 24 kilometres per litre and standard deviation 4.7 kilometres per litre. Find the probability that the petrol consumption of a randomly chosen car of this type is between 21.6 kilometres per litre and 28.7 kilometres per litre.

\hfill \mbox{\textit{CAIE S1 2014 Q1 [4]}}
This paper (7 questions)
View full paper
Q1 4 Q2 5 Q3 5 Q4 7 Q5 8 Q6 10 Q7 11