CAIE S1 2013 November — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeSingle tail probability P(X < a) or P(X > a)
DifficultyEasy -1.2 This is a straightforward single-step normal distribution problem requiring only standardization using z = (x - μ)/σ and table lookup. It involves no problem-solving, just direct application of the standard procedure for finding P(X < a), making it easier than average.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
1 It is given that \(X \sim \mathrm {~N} \left( 1.5,3.2 ^ { 2 } \right)\). Find the probability that a randomly chosen value of \(X\) is less than - 2.4 .
AnswerMarks Guidance
\(P(x < -2.4) = P\left(z < \frac{-2.4 - 1.5}{3.2}\right)\)M1 Standardising, no cc can have sq
\(= P(z < -1.219) = 1 - 0.8886 = 0.111\)M1 Correct area, i.e. < 0.5
A1 [3]Correct answer rounding to 0.111 
$P(x < -2.4) = P\left(z < \frac{-2.4 - 1.5}{3.2}\right)$ | M1 | Standardising, no cc can have sq

$= P(z < -1.219) = 1 - 0.8886 = 0.111$ | M1 | Correct area, i.e. < 0.5

| A1 [3] | Correct answer rounding to 0.111
1 It is given that $X \sim \mathrm {~N} \left( 1.5,3.2 ^ { 2 } \right)$. Find the probability that a randomly chosen value of $X$ is less than - 2.4 .

\hfill \mbox{\textit{CAIE S1 2013 Q1 [3]}}
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