AQA Further AS Paper 2 Statistics 2024 June — Question 3 3 marks

Exam BoardAQA
ModuleFurther AS Paper 2 Statistics (Further AS Paper 2 Statistics)
Year2024
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentral limit theorem
TypeKnown variance confidence intervals
DifficultyModerate -0.8 This is a straightforward application of the confidence interval formula for known variance with all values provided. Students only need to recall the formula, look up the z-value for 94%, and substitute into x̄ ± z×(σ/√n). No conceptual difficulty or problem-solving required—purely mechanical calculation.
Spec5.05d Confidence intervals: using normal distribution
3 The random variable \(X\) has a normal distribution with known variance 15.7 A random sample of size 120 is taken from \(X\) The sample mean is 68.2 Find a 94\% confidence interval for the population mean of \(X\) Give your limits to three significant figures.
Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
Correct \(z\) value, AWRT \(1.88\), or correct \(t\) value, AWRT \(1.90\)B1 AO 1.1b; PI
Uses formula \(\bar{x} \pm z \times \sqrt{\dfrac{s^2}{n}}\) for upper or lower limit using their \(z\) or \(t\) valueM1 AO 1.1a; PI
\(68.2 \pm 1.8808 \times \sqrt{\dfrac{15.7}{120}}\), giving correct interval AWRT \((67.5, 68.9)\)A1 AO 1.1b
Question total: 3 marks
## Question 3:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct $z$ value, AWRT $1.88$, or correct $t$ value, AWRT $1.90$ | B1 | AO 1.1b; PI |
| Uses formula $\bar{x} \pm z \times \sqrt{\dfrac{s^2}{n}}$ for upper or lower limit using their $z$ or $t$ value | M1 | AO 1.1a; PI |
| $68.2 \pm 1.8808 \times \sqrt{\dfrac{15.7}{120}}$, giving correct interval AWRT $(67.5, 68.9)$ | A1 | AO 1.1b |

**Question total: 3 marks**
3 The random variable $X$ has a normal distribution with known variance 15.7

A random sample of size 120 is taken from $X$

The sample mean is 68.2

Find a 94\% confidence interval for the population mean of $X$

Give your limits to three significant figures.\\

\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2024 Q3 [3]}}
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