Question 1 - A-Level Maths

CAIE S1 2016 November — Question 1 3 marks

Exam Board	CAIE
Module	S1 (Statistics 1)
Year	2016
Session	November
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Normal Distribution
Type	Find k given probability statement
Difficulty	Moderate -0.8 This is a straightforward inverse normal distribution problem requiring only a single step: look up the z-value for upper quartile (0.674) and apply the transformation k = μ + zσ = 20 + 0.674(7). It tests basic understanding of normal distribution with no problem-solving or multi-step reasoning required.
Spec	2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation

1 The random variable \(X\) is such that \(X \sim \mathrm {~N} ( 20,49 )\). Given that \(\mathrm { P } ( X > k ) = 0.25\), find the value of \(k\).

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Question 1:

Answer	Marks	Guidance
\(z = 0.674\)	M1	±0.674 seen
\(0.674 = \frac{k-20}{7}\)	M1	Standardising no cc, no sq, no sq rt
\(k = 24.7\)	A1

[3]

Question 1:

$z = 0.674$ | M1 | ±0.674 seen

$0.674 = \frac{k-20}{7}$ | M1 | Standardising no cc, no sq, no sq rt

$k = 24.7$ | A1

[3]

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1 The random variable $X$ is such that $X \sim \mathrm {~N} ( 20,49 )$. Given that $\mathrm { P } ( X > k ) = 0.25$, find the value of $k$.

\hfill \mbox{\textit{CAIE S1 2016 Q1 [3]}}

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