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Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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12 questions

SA-9709-P6-SE-0091 markL1 FoundationCalculatorCLT
The Central Limit Theorem says that, for a large sample from any population with mean μ\mu and variance σ2\sigma^2,
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0013 marksL1 FoundationCalculatorNormal sample means
X∼N(60,16)X\sim N(60,16). A random sample of 44 observations is taken. Find P(Xˉ<57)P(\bar X<57), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0021 markL1 FoundationCalculatorCLT
A population has standard deviation 1010. Find the standard deviation of the mean of a random sample of 2525.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0051 markL1 FoundationCalculatorCLT
In which situation is the Central Limit Theorem needed?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE-0023 marksL2 StandardCalculatorNormal sample means
X∼N(100,152)X\sim N(100,15^2). A random sample of 2525 is taken. Find P(Xˉ>104)P(\bar X>104), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE-0033 marksL2 StandardCalculatorCLT
A population (not necessarily normal) has mean 5050 and standard deviation 88. A random sample of 6464 is taken. Find, approximately, P(Xˉ<48.5)P(\bar X<48.5), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE-0112 marksL2 StandardCalculatorCLT
XX has standard deviation 1212. Find the standard deviation of the mean of a random sample of 3636 values.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0033 marksL2 StandardCalculatorCLT
A population with an unknown distribution has mean 3030 and standard deviation 66. A random sample of 5050 is taken. Find, approximately, P(Xˉ>31)P(\bar X>31), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0043 marksL2 StandardCalculatorNormal sample means
X∼N(200,252)X\sim N(200,25^2). A random sample of 1616 is taken. Find P(195<Xˉ<205)P(195<\bar X<205), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0062 marksL2 StandardCalculatorNormal sample means
A population has standard deviation 77. Find the smallest sample size nn for which the standard deviation of Xˉ\bar X is less than 11.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0082 marksL2 StandardCalculatorNormal sample means
X∼N(μ,9)X\sim N(\mu,9). A random sample of 3636 is taken. Find the probability that Xˉ\bar X is more than 11 above μ\mu, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-SE2-0074 marksL3 ExamCalculatorCLT
X∼Po(4)X\sim\text{Po}(4). A random sample of 4040 observations is taken. Use a suitable approximation to find P(Xˉ>4.5)P(\bar X>4.5), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme